Class: Quasi::NX

Inherits:

LowDiscrepancySequence

• Object
• LowDiscrepancySequence
• Quasi::NX

Defined in:

lib/NX.rb

Instance Method Summary

• #getName ⇒ Object

  end constructor.

• #gMC ⇒ Object

  Generator matrix array.

• #initialize(dim) ⇒ NX constructor

  constructor.

• #nextPoint ⇒ Object
• #restart ⇒ Object

  The NX points.

Methods inherited from LowDiscrepancySequence

#L2_discrepancy, #n_inverse, #nextQuasiNormalVector, #product, #productSQ, #projectionOut

Constructor Details

#initialize(dim) ⇒ NX

constructor

# File 'lib/NX.rb', line 15

def initialize(dim)
  super(dim)
  #check for max dimension
  d=[dim,4].max
 #puts gMC.inspect 
  @genMats=gMC[d-4]
  @M=30 
   @N=2.0**30
  # array of current nx-integers
  @x_int= Array.new(dim)
  for j in 0..dim-1
    @x_int[j]=@genMats[j][0]
  end    
  
end

Instance Method Details

#getName ⇒ Object

end constructor

# File 'lib/NX.rb', line 31

def getName
  return "NX-sequence"  
end

#gMC ⇒ Object

Generator matrix array

# File 'lib/NX.rb', line 64

def gMC
  x=[[[939524096,771751936,729808896,182452224,582483968,145620992,
  573276160,143319040,35829760,8957440,539110272,134777568,
  33694392,8423598,538976811,134744202,33686050,8421512,
  2105378,526344,131586,32896,536879136,134219784,
  33554946,8388736,2097184,524296,131074,32768],
  [1010580540,698984873,501358050,723004184,463969191,571187723,
  132511770,185808928,465315712,573148032,127769215,195797171,
  437911997,538968619,8386661,11745427,29107772,36276649,
  127770082,195799832,437918631,538976779,8357861,11766547,
  29203389,36413995,127535002,195038112,436214272,536879104],
 [757935405,151587081,835596750,582689467,53347118,34275851,
  1007535090,722055824,842080028,539109675,3944946,2826896,
  3277596,2097707,1069548493,699400889,823919405,573243913,
  1009925134,723528459,838873650,536879136,16320,10672,
  12572,8747,15410,11040,12800,8192],
  [469762048,721420288,230686720,162529280,823918592,573243392,
  63815680,45723648,53287936,34155264,1007553984,722143664,
  842150172,538976811,4178893,2732729,3219245,2238729,
  3944910,2826939,3277614,2097675,1069548530,699400848,
  823919388,573243947,1009925170,723528480,838873600,536879104]],   
 [[713031680,1028653056,276430848,620052480,854321152,1063687424,
  832587680,1045106516,468108990,593634153,455302564,588966884,
  831404242,508908875,570011537,447011402,58925105,22147102,
  711520267,1027043335,274395139,619589633,853889316,526625828,
  556899090,450414731,61695349,22003374,711319143,1026803237],
  [469762048,301989888,897581056,37748736,556793856,872939520,
  43384832,558432256,339001344,370679808,924604416,51127296,
  563352320,340279424,371599712,922817680,587236172,352338306,
  377498053,390075586,934283841,55051268,565463810,341337217,
  372011844,923021702,587340231,352404675,377528897,390090756],
  [444180378,582771426,386103319,820878768,768469037,464323199,
  540534784,147816993,431574890,613378415,440641348,585935378,
  231724032,321626113,957130649,762735301,11922288,24841932,
  431584074,613353990,440628151,585993112,231593821,321875383,
  956409753,761948869,9300848,19861196,419525450,636044067],
  [874725940,276345168,1005962939,404842328,44797378,390406220,
  719975565,573261292,995508545,418874694,907865252,322234891,
  226350248,200248046,996057078,201936327,719123621,922205246,
  327333406,761281382,321461212,767251478,664019960,1027015197,
  482492772,825457823,37181888,54617459,914535782,331364768],
  [1010287484,387092183,210512716,885098740,230022349,551664607,
  58382349,737801095,851645666,472257767,20236143,1039091209,
  58775360,44000576,1061407804,1021417497,1044512992,686817112,
  210706479,885241161,830590908,506889871,1048831907,677547034,
  209243052,497930786,3673294,3045292,1006772076,389294580]],
  
  #dimension 6
  [

  [644587520,320281088,403904282,548421841,437785367,394981521,
  506554803,530293121,648244152,185106849,11569178,557480225,
  973123720,361462440,504459536,142843915,545798656,337900032,
  1040972186,196311331,413671560,562725384,572041248,35752578,
  2234536,139658,8728,556888961,973078562,898331042],

  [685031084,856664270,430555838,298298601,984050532,453855559,
  613834890,991631314,1068941538,74048175,151788468,813918083,
  973205740,441353078,646982048,835775508,562397940,735494680,
  129726984,352099622,830745068,555559847,2216356,5036425,
  10885656,21140430,33858208,537335420,453587814,441440925],

  [628217850,325454664,998314354,268731841,453835512,758493955,
  558219927,493683099,988488409,366666052,736178184,809509177,
  462094524,742319014,574824549,633529913,188824518,221007958,
  560132781,96960952,818606902,554926544,52675512,80590561,
  139458802,290959604,589418696,537223600,999014834,742375611],

  [448749995,998890424,413198730,94371370,334225648,107954880,
  955423729,849826956,143809279,92746299,191107394,559297372,
  464313148,388043114,458511115,558604207,53072112,660938837,
  995508297,349305116,810412340,538757973,2568240,4249692,
  9384126,18320328,58841356,827833309,992673974,371872246],

  [990132955,386692475,335605549,861087837,982651609,84928281,
  6917107,513462859,927225443,147357176,230147361,580863685,
  400855275,1050928175,593828120,332815393,779729968,513430758,
  591690417,173375938,441512876,572594787,53330721,44572176,
  63823260,35170609,51159688,719696755,445730208,84769844],

  [499122176,447741952,925761536,176029696,962341888,302734336,
  376373248,62016864,205310848,834126720,762654859,423141431,
  399325739,730034628,911033337,334795476,777243070,197128747,
  913256528,3945220,923566130,431370928,537112076,826011012,
  764805349,994803843,602680533,293929560,443642261,284450072]

  ],
  
  #dimension 7
  [

  [644587520,320281088,403904282,548421841,437785367,394981521,
  506554803,530293121,648244152,185106849,11569178,557480225,
  973123720,361462440,504459536,142843915,545798656,337900032,
  1040972186,196311331,413671560,562725384,572041248,35752578,
  2234536,139658,8728,556888961,973078562,898331042],

  [685031084,856664270,430555838,298298601,984050532,453855559,
  613834890,991631314,1068941538,74048175,151788468,813918083,
  973205740,441353078,646982048,835775508,562397940,735494680,
  129726984,352099622,830745068,555559847,2216356,5036425,
  10885656,21140430,33858208,537335420,453587814,441440925],

  [628217850,325454664,998314354,268731841,453835512,758493955,
  558219927,493683099,988488409,366666052,736178184,809509177,
  462094524,742319014,574824549,633529913,188824518,221007958,
  560132781,96960952,818606902,554926544,52675512,80590561,
  139458802,290959604,589418696,537223600,999014834,742375611],

  [448749995,998890424,413198730,94371370,334225648,107954880,
  955423729,849826956,143809279,92746299,191107394,559297372,
  464313148,388043114,458511115,558604207,53072112,660938837,
  995508297,349305116,810412340,538757973,2568240,4249692,
  9384126,18320328,58841356,827833309,992673974,371872246],

  [990132955,386692475,335605549,861087837,982651609,84928281,
  6917107,513462859,927225443,147357176,230147361,580863685,
  400855275,1050928175,593828120,332815393,779729968,513430758,
  591690417,173375938,441512876,572594787,53330721,44572176,
  63823260,35170609,51159688,719696755,445730208,84769844],

  [499122176,447741952,925761536,176029696,962341888,302734336,
  376373248,62016864,205310848,834126720,762654859,423141431,
  399325739,730034628,911033337,334795476,777243070,197128747,
  913256528,3945220,923566130,431370928,537112076,826011012,
  764805349,994803843,602680533,293929560,443642261,284450072],

  [394486004,974886838,170929084,939407551,831916941,1059229394,
  328736998,51297358,557459938,178298032,143307296,901863802,
  967646216,901529372,455215978,1069593776,999700512,925375062,
  328241918,10271058,176291970,34081282,134219784,178954250,
  142772744,167903914,134744194,896126085,958899621,1068804408]

  ],
  
  # DIMENSION dim=8,  generator matrices column encodings:

  [

  [760554632,893269568,1018726252,397550846,486706887,709025900,
  691463814,897059424,771925038,48245314,445661732,365996202,
  738733570,180388576,964722734,537575554,167816200,144706240,
  723044396,895150218,771787264,48236704,137232522,142794760,
  8924672,557792,448710830,500318210,747110536,180912136],

  [191925899,850322866,184392687,549799844,1024443066,576347035,
  382532166,16627116,182150555,475711155,390430684,312432314,
  738311052,271793309,380782643,1020390196,815275293,540233864,
  292597895,239456792,478389643,808653086,557457846,40619436,
  129541521,246531490,821638469,472330680,978942525,1012590597],

  [883717684,96518021,652853286,466291355,693221929,545287968,
  966891722,388157465,457902881,1043440021,767486751,96647075,
  1015198876,817049866,59417384,1020938648,805505024,537001984,
  943048725,356580925,487641606,853040652,664254599,238742324,
  399224619,780317982,208309733,119593013,994773809,1043440053],

  [527160192,861192064,574201038,56565168,4568205,48833925,
  95077866,255844538,189274428,503510557,792005641,294530466,
  1024051984,853178650,1028795142,806055692,538444458,3240220,
  35861445,17606958,478325819,817042729,567019160,48393984,
  131186604,243438122,247019859,334236546,995232528,1043571127],

  [966096851,159603416,391853503,534263005,567925083,754632580,
  605300517,525481798,749929250,951300503,831759277,730950479,
  90347043,911409212,381929330,911329204,459292567,581683098,
  776501376,328445808,627119239,911278881,459320868,581640838,
  848849327,746103428,695461275,185665125,882556987,411067682],

  [592598110,477898738,153058420,620511864,746949233,214503603,
  1035856176,135138758,748241599,948069951,742923334,312806868,
  1040260755,351989255,286634848,439053624,592972212,44821798,
  935742183,83151353,626597915,911288994,458790296,581632030,
  848845844,746096664,881612722,840751721,266897418,974806028],

  [814597320,726846282,153113138,530614223,894963566,209244070,
  761266718,1027120870,391299851,447447865,651951006,624563529,
  109126031,888852356,141706978,447434656,600454415,44812218,
  658370173,830073561,506161194,348721804,695606583,241751322,
  179316754,214663084,1035206920,128477917,884028701,405904022],

  [212183505,575897462,674724232,907724773,335232225,249625608,
  406679306,978524888,801158541,983070477,82256637,246020036,
  111731374,885723697,756331345,445791144,601390858,43522354,
  290858668,872585938,626715393,912326453,458692903,580025402,
  842012457,751523504,529968469,738202308,884017946,405909655]

  ],

  # DIMENSION dim=9,  generator matrices column encodings:

  [

  [696344576,177875968,198830848,332466784,765128780,786752711,
  700394490,710743797,80402060,582321570,531330516,600994053,
  250343324,166325309,469206004,127787017,350209407,959505056,
  402000190,101740930,58507941,533330381,53139563,235760460,
  927807685,1048967523,1039779877,893524859,774165468,417325468],

  [912973312,273086528,1043348344,304024545,144844181,373870990,
  620509713,1032943564,953994563,579754739,988202473,136063485,
  174254401,979221296,243294609,210750988,191980114,384136855,
  119830278,960709408,152810196,87797445,725033016,935489600,
  513691672,375388711,601961381,646256774,844711761,782078212],

  [1070658743,541351219,177168414,857506082,954298862,189990685,
  928237287,714563635,825097568,486326679,620190618,234665099,
  969800906,10921771,117651574,960455758,712481989,104218246,
  49191030,395016413,243053293,50889952,533282744,507581774,
  365648082,362117277,943766598,452105566,134382757,600036003],

  [468149054,356323242,531691055,533479845,369430665,1050335897,
  855633172,121777424,926972951,861803436,633315042,147299592,
  44904118,716540604,848053812,161692489,18786120,175446231,
  329890245,289816975,992443882,144833905,280706725,393983156,
  1024471095,244194217,705811717,343438231,1010252774,369916015],

  [47463531,688500491,156046897,840884700,909106686,269785563,
  239678700,930221356,503006993,979373410,786124814,22097096,
  585759744,310525712,75113259,233079227,876226168,352865085,
  796223239,120697769,233031239,848080728,960129683,786952936,
  709641922,119053788,66120245,256432093,854840906,1062655013],

  [823931987,369032796,955029757,104856506,770334010,240341623,
  205772931,911259079,915206596,930217353,690026418,625901845,
  48782362,390178869,852575964,836019537,694715425,89906349,
  150902223,5834217,11009007,485593977,400623134,1069427788,
  691791464,405765657,1019838073,551252580,986644545,225903139],

  [382091319,739313283,942124987,288243186,229802861,751574681,
  41151136,730405574,502619122,149340930,382496547,383277427,
  951451155,587583426,191540436,308805631,1064908987,81380314,
  127274604,62709513,46705551,1032153411,829062413,747188657,
  444648745,199504873,237992630,378356548,772791966,833105476],

  [587078599,203960422,511194114,755679438,139542925,28367724,
  165315148,768111470,999912497,1027667728,638438543,359237201,
  196888839,463057534,268847481,214959631,431660447,480659247,
  337817622,224901951,151877581,263454068,928091576,989398959,
  722566738,924770779,629317449,713695576,181619785,564028034],

  [453809691,380853116,899434263,666973159,182611982,1008223646,
  637955544,153759368,411114377,566828272,44056958,585359217,
  34385615,801789890,507572939,48458184,992087037,411762415,
  286362362,826271647,604665201,298685982,211695003,664079058,
  265179510,352453822,1031228380,533517717,914087299,668725875]

  ],

  # DIMENSION dim=10,  generator matrices column encodings:

  [

  [696344576,177875968,198830848,332466784,765128780,786752711,
  700394490,710743797,80402060,582321570,531330516,600994053,
  250343324,166325309,469206004,127787017,350209407,959505056,
  402000190,101740930,58507941,533330381,53139563,235760460,
  927807685,1048967523,1039779877,893524859,774165468,417325468],

  [912973312,273086528,1043348344,304024545,144844181,373870990,
  620509713,1032943564,953994563,579754739,988202473,136063485,
  174254401,979221296,243294609,210750988,191980114,384136855,
  119830278,960709408,152810196,87797445,725033016,935489600,
  513691672,375388711,601961381,646256774,844711761,782078212],

  [1070658743,541351219,177168414,857506082,954298862,189990685,
  928237287,714563635,825097568,486326679,620190618,234665099,
  969800906,10921771,117651574,960455758,712481989,104218246,
  49191030,395016413,243053293,50889952,533282744,507581774,
  365648082,362117277,943766598,452105566,134382757,600036003],

  [468149054,356323242,531691055,533479845,369430665,1050335897,
  855633172,121777424,926972951,861803436,633315042,147299592,
  44904118,716540604,848053812,161692489,18786120,175446231,
  329890245,289816975,992443882,144833905,280706725,393983156,
  1024471095,244194217,705811717,343438231,1010252774,369916015],

  [47463531,688500491,156046897,840884700,909106686,269785563,
  239678700,930221356,503006993,979373410,786124814,22097096,
  585759744,310525712,75113259,233079227,876226168,352865085,
  796223239,120697769,233031239,848080728,960129683,786952936,
  709641922,119053788,66120245,256432093,854840906,1062655013],

  [823931987,369032796,955029757,104856506,770334010,240341623,
  205772931,911259079,915206596,930217353,690026418,625901845,
  48782362,390178869,852575964,836019537,694715425,89906349,
  150902223,5834217,11009007,485593977,400623134,1069427788,
  691791464,405765657,1019838073,551252580,986644545,225903139],

  [382091319,739313283,942124987,288243186,229802861,751574681,
  41151136,730405574,502619122,149340930,382496547,383277427,
  951451155,587583426,191540436,308805631,1064908987,81380314,
  127274604,62709513,46705551,1032153411,829062413,747188657,
  444648745,199504873,237992630,378356548,772791966,833105476],

  [587078599,203960422,511194114,755679438,139542925,28367724,
  165315148,768111470,999912497,1027667728,638438543,359237201,
  196888839,463057534,268847481,214959631,431660447,480659247,
  337817622,224901951,151877581,263454068,928091576,989398959,
  722566738,924770779,629317449,713695576,181619785,564028034],

  [453809691,380853116,899434263,666973159,182611982,1008223646,
  637955544,153759368,411114377,566828272,44056958,585359217,
  34385615,801789890,507572939,48458184,992087037,411762415,
  286362362,826271647,604665201,298685982,211695003,664079058,
  265179510,352453822,1031228380,533517717,914087299,668725875],

  [931239939,828945438,363684192,95705596,248262652,526274471,
  61950506,542401026,593450089,139006496,220316088,1019960300,
  192398181,834630841,1072820851,474696622,1017601997,925673718,
  774313960,12886932,8871591,362158636,293953661,573034866,
  595008664,935547810,757597401,7383456,476631037,577177943]

  ],

  # DIMENSION dim=11,  generator matrices column encodings:

  [

  [640076413,38619923,880276074,258462862,218061951,110875386,
  782095512,253820603,543879802,1050676528,655726172,1061996849,
  738961624,599680434,1010784250,414752449,180264169,676013088,
  361315153,950490779,626020133,142567564,521541876,618804908,
  178037201,362432873,391430156,528491869,1063457085,141830450],

  [393823488,967702564,996414134,380720145,300495822,884499191,
  768736405,91406721,741603631,624224565,359456934,89283930,
  537918092,829699217,349844160,264781100,1031472974,300442722,
  219489904,623147931,359027908,503369389,414890524,46246130,
  734200851,550896721,990511752,756780245,917175879,319155042],

  [606494016,917965809,1018376187,163092929,747799491,115078791,
  939997329,17414853,302426061,921867709,602154136,999186600,
  411725464,223769413,703344350,841532862,797735996,1020553390,
  1009041997,950379831,627636356,178720078,409380538,70557298,
  673255255,835970611,286203702,266426382,560101456,39390863],

  [600866816,685960568,103280453,309088841,955194087,1044309885,
  605453218,957769029,348362389,812806796,302838834,313274906,
  300197590,275279179,332855626,37604359,698428890,206208084,
  238230667,367047777,4381534,735883523,1064951460,203911503,
  78225905,998688573,340732841,941500948,201590684,371703833],

  [346200071,734643499,123089088,649304842,605054314,790301134,
  48561423,242319144,801905870,66727240,424813982,158270750,
  162634162,146649881,731766097,380723582,33118141,861489947,
  741323110,237146728,263233061,427681584,870037056,474509960,
  337598642,712260834,886629205,541733652,450393070,280197089],

  [986274698,148131086,870716920,447282332,1026196869,472749574,
  32460871,272231963,410368694,178649215,888633116,1041483275,
  940674463,931538664,956736924,524225383,936411974,969547861,
  512648518,381104443,205372356,13905180,333072039,496115283,
  546594229,1065067452,179675074,227185735,993747182,39536207],

  [261598117,611550090,211615492,100722117,634969513,368972092,
  686506470,533599043,530639277,873784702,575933634,411444686,
  102047956,816671590,1010229544,185842073,978642477,562673342,
  1003690264,941331870,814018105,637603710,143573597,1037408318,
  307920125,339901701,832688107,722546136,412159266,769219252],

  [922063332,565134652,82071906,769088394,944402391,138740959,
  433429701,862296561,993983047,899835002,1037945714,417060381,
  752393547,88184049,966044098,680894913,514682970,719476347,
  886465807,486029512,62535029,555167353,307430836,709660495,
  1041707699,786398307,825953853,750169210,221302275,595424191],

  [512467929,300113655,674083661,689445985,148105911,866522716,
  313630486,395717289,301814491,655585295,577555299,917231748,
  888920033,927718938,724360554,377554296,248732447,174080875,
  559178264,89877466,399554243,298097523,363683154,825448247,
  854096856,766321194,215392664,646036130,1892589,311854397],

  [986027855,132090846,621223411,333974992,790598050,79387364,
  267995867,599454495,232907008,15913258,302191763,772790356,
  584503088,738046272,188438137,921819200,697430148,137752459,
  873342196,227078802,442976560,1034616614,172909972,40524786,
  747034583,462482257,28803124,462481449,885322935,182269347],

  [648793944,607217858,974232141,283030681,2576790,535183650,
  157523670,496460795,334546972,8482709,896794205,786499822,
  228269069,998643015,607626918,151122715,717253132,1010802792,
  529041112,437142038,545850927,663932102,587251879,161482998,
  958459306,918804181,617570748,471288770,418354821,666780001]

  ],

  # DIMENSION dim=12,  generator matrices column encodings:

  [

  [376009787,616649261,1038915818,449176030,680969485,844929903,
  469210199,515424615,955287332,441067371,672960609,10667578,
  518196311,909235475,829362448,606869120,1069286697,548650217,
  281564703,956233651,30374325,339266501,406232992,308994419,
  308329741,419071262,157656941,113798237,580526181,312086276],

  [113325173,802884388,776006141,240665347,1067428575,237210076,
  433405280,542548953,206172120,892707582,938920668,268533774,
  427179081,64599497,584946987,850670289,1029168313,406383405,
  567739064,243337945,534671208,284667432,604603719,624171720,
  638094189,480469014,81680586,875930397,165521623,713379925],

  [365589568,795832513,352548612,791353731,639030956,875424815,
  460322970,209202842,769072557,62593514,554917907,422257425,
  988433200,845378618,964807902,469755058,490235585,36511719,
  305707082,338554719,877932899,475033153,48231578,414880648,
  706291263,70011941,255603371,718605877,1049680271,203585716],

  [435632494,172170459,1059343654,565249317,65081497,498668119,
  696359679,815656005,627318345,886975033,230810440,958457568,
  170678992,928599693,50537551,95312547,130331293,202074131,
  1045327915,1032883628,259200551,538263735,525010700,117358056,
  867099869,70373620,495094033,522626779,38232465,95758096],

  [32678341,505635296,425856624,1054825470,1033723186,938870058,
  269291076,814524247,656722885,524631983,597477638,436880436,
  697998740,64815620,786707110,297283695,494619587,996221642,
  743211695,532501720,485366627,575598237,246747572,221087582,
  195011953,225867526,624744711,494497451,771083163,465002468],

  [551397128,489766929,195538897,629476791,1006219829,921379579,
  836280603,978070866,1007507930,236561171,759639615,439796207,
  338293708,24298018,558561689,657466702,188516653,553216800,
  981177690,1010977003,791689962,158536313,388269785,487774813,
  224170145,624982216,529627459,530281195,133158627,81743442],

  [768717957,184677116,591120478,258801695,981458210,434399026,
  697605612,787798639,845498401,27242131,198461923,975748095,
  873564500,808362448,829314929,599428700,553956900,646455049,
  715447491,990180123,901857731,341740714,518651244,433436011,
  393492963,156099629,1014527846,267932060,338771950,491714313],

  [609470369,578981355,496170689,646129714,870096655,49561033,
  642998690,66791072,319166205,892427797,521637492,815247648,
  244676424,701940472,831147871,570779345,89071257,880115963,
  152451089,13233731,318042497,408461437,1007221712,775537592,
  174347183,811508503,942904086,319793289,566294292,956161085],

  [690191426,28134813,207393949,406243981,500443338,244003934,
  327631593,692702121,76532237,120264433,305592447,23783510,
  936434940,129432986,891044703,133326731,759067238,805090750,
  393846010,895707158,773285066,682629395,68829201,219221301,
  116077786,1009888418,978576807,641438017,169610131,526023641],

  [226253065,147381635,1009733192,730981142,441127473,1068685129,
  902159719,362034294,888137773,862283775,338017958,22628013,
  340658897,130197395,630654134,42912700,324565062,640826151,
  540055184,214577500,940181002,475921976,880471073,962578486,
  937098890,1035691007,496051649,546273064,104382506,758339435],

  [980220447,391809923,926256294,896109598,310914840,979419742,
  492998431,917440954,1036679165,877461802,482469020,413101932,
  360109925,34299936,186285141,291647287,420363989,406330999,
  854416866,979161387,721088013,775806082,25986602,601668135,
  282692574,256034532,1047609668,427797668,402427615,284346209],

  [805428583,869599887,1014763568,659252565,973942038,754651348,
  897847746,182137879,679510472,128246679,807357794,396531141,
  578604545,486979889,898367645,336668900,827682136,327305202,
  213888167,744078157,351257983,316843621,473816217,495813680,
  483886281,885162661,246466767,823380730,817597230,113843058]

  ],

  # DIMENSION dim=13,  generator matrices column encodings:

  [

  [376009787,616649261,1038915818,449176030,680969485,844929903,
  469210199,515424615,955287332,441067371,672960609,10667578,
  518196311,909235475,829362448,606869120,1069286697,548650217,
  281564703,956233651,30374325,339266501,406232992,308994419,
  308329741,419071262,157656941,113798237,580526181,312086276],

  [113325173,802884388,776006141,240665347,1067428575,237210076,
  433405280,542548953,206172120,892707582,938920668,268533774,
  427179081,64599497,584946987,850670289,1029168313,406383405,
  567739064,243337945,534671208,284667432,604603719,624171720,
  638094189,480469014,81680586,875930397,165521623,713379925],

  [365589568,795832513,352548612,791353731,639030956,875424815,
  460322970,209202842,769072557,62593514,554917907,422257425,
  988433200,845378618,964807902,469755058,490235585,36511719,
  305707082,338554719,877932899,475033153,48231578,414880648,
  706291263,70011941,255603371,718605877,1049680271,203585716],

  [435632494,172170459,1059343654,565249317,65081497,498668119,
  696359679,815656005,627318345,886975033,230810440,958457568,
  170678992,928599693,50537551,95312547,130331293,202074131,
  1045327915,1032883628,259200551,538263735,525010700,117358056,
  867099869,70373620,495094033,522626779,38232465,95758096],

  [32678341,505635296,425856624,1054825470,1033723186,938870058,
  269291076,814524247,656722885,524631983,597477638,436880436,
  697998740,64815620,786707110,297283695,494619587,996221642,
  743211695,532501720,485366627,575598237,246747572,221087582,
  195011953,225867526,624744711,494497451,771083163,465002468],

  [551397128,489766929,195538897,629476791,1006219829,921379579,
  836280603,978070866,1007507930,236561171,759639615,439796207,
  338293708,24298018,558561689,657466702,188516653,553216800,
  981177690,1010977003,791689962,158536313,388269785,487774813,
  224170145,624982216,529627459,530281195,133158627,81743442],

  [768717957,184677116,591120478,258801695,981458210,434399026,
  697605612,787798639,845498401,27242131,198461923,975748095,
  873564500,808362448,829314929,599428700,553956900,646455049,
  715447491,990180123,901857731,341740714,518651244,433436011,
  393492963,156099629,1014527846,267932060,338771950,491714313],

  [609470369,578981355,496170689,646129714,870096655,49561033,
  642998690,66791072,319166205,892427797,521637492,815247648,
  244676424,701940472,831147871,570779345,89071257,880115963,
  152451089,13233731,318042497,408461437,1007221712,775537592,
  174347183,811508503,942904086,319793289,566294292,956161085],

  [690191426,28134813,207393949,406243981,500443338,244003934,
  327631593,692702121,76532237,120264433,305592447,23783510,
  936434940,129432986,891044703,133326731,759067238,805090750,
  393846010,895707158,773285066,682629395,68829201,219221301,
  116077786,1009888418,978576807,641438017,169610131,526023641],

  [226253065,147381635,1009733192,730981142,441127473,1068685129,
  902159719,362034294,888137773,862283775,338017958,22628013,
  340658897,130197395,630654134,42912700,324565062,640826151,
  540055184,214577500,940181002,475921976,880471073,962578486,
  937098890,1035691007,496051649,546273064,104382506,758339435],

  [980220447,391809923,926256294,896109598,310914840,979419742,
  492998431,917440954,1036679165,877461802,482469020,413101932,
  360109925,34299936,186285141,291647287,420363989,406330999,
  854416866,979161387,721088013,775806082,25986602,601668135,
  282692574,256034532,1047609668,427797668,402427615,284346209],

  [805428583,869599887,1014763568,659252565,973942038,754651348,
  897847746,182137879,679510472,128246679,807357794,396531141,
  578604545,486979889,898367645,336668900,827682136,327305202,
  213888167,744078157,351257983,316843621,473816217,495813680,
  483886281,885162661,246466767,823380730,817597230,113843058],

  [775536582,900718787,360197547,657428423,989613149,276818072,
  35434343,207452155,929686556,379446274,350997024,403659830,
  201733068,183406655,581133571,783416532,685549740,39396776,
  872208726,306668169,749911467,1003397486,871981435,563905409,
  1059652571,635124084,913427898,606299715,882851360,902877678]

  ],

  # DIMENSION dim=14,  generator matrices column encodings:

  [

  [122455510,773296462,80386005,883424770,513326595,981703937,
  1038812148,243570348,778200383,102755401,595654303,880576513,
  296182727,1055400600,996075111,1052355578,964134372,482021623,
  1010269190,146064639,699374654,545735549,783309448,241955223,
  391613045,316095920,691188546,107203704,913774004,919011693],

  [904829865,125800112,744836867,56211074,962495785,1014331605,
  31766538,1036440779,378917045,863948098,170171268,150539741,
  291559995,144340146,936281598,725120753,165033544,957473065,
  142516263,917214920,406122355,215612829,806188527,444563495,
  94075866,902187783,921358076,515829670,842057841,754580171],

  [144252053,719681002,764865240,360782177,8473587,170796252,
  322670896,824841090,715394417,308461745,767985005,603286018,
  282278856,370444133,799573691,207061925,378626792,443460925,
  747932389,190656701,112052892,838906526,456638239,308815925,
  314952227,615497055,197589208,851292505,114291449,749275465],

  [508763882,863822867,579200240,341866102,1020791415,952571345,
  739394084,867999885,527833410,840385800,558226716,581629303,
  539677350,61386309,344675504,571043943,679597514,131099271,
  983978597,401123019,825124467,1023625675,887540408,932091587,
  134304604,538330537,662740073,203901635,988267545,346153028],

  [621391692,190216341,240288833,47344896,848418599,660064937,
  724208392,17567804,947270235,290260854,65728614,661215123,
  409991240,708141568,308244599,200143731,276033077,525109062,
  395293500,464968947,618144500,326508566,615516113,557986837,
  45672459,435884540,701004880,63546760,785500141,862516802],

  [943528403,7424764,444055955,410453694,92186155,283874613,
  17575750,133964545,995073250,957980469,277245753,188272488,
  587777482,95089141,581464409,824556694,437316241,640484097,
  696373407,412102094,239622123,522038752,228604636,453088305,
  1071365639,498667903,869393790,449562132,1033358097,817761061],

  [1023859687,860420336,437777716,959192061,251318774,343778092,
  413416680,259452981,676804407,122487975,95708507,1054678216,
  363422616,466995666,325488046,373888941,515222328,781087025,
  997868815,459829544,41014936,226257344,331113322,597700410,
  963882199,450825004,1020970018,804124363,40896571,505564148],

  [755137672,742859173,936475141,354522321,797948600,730638890,
  204492398,159152738,471715321,123471289,839297694,642348689,
  750583992,76497646,744562819,577560611,139554140,626389783,
  521865008,377281746,344637867,286741651,324330987,196287246,
  804548810,417370381,309802854,984272094,97243419,1025617989],

  [510369304,236761812,13110549,616873707,521953617,792634244,
  531230079,775306128,407484179,747791618,694386176,331508215,
  818343003,781023012,308300789,805796298,944521705,592032883,
  269937303,405771211,145315315,973429799,145186174,1009885150,
  723080138,412171449,770686949,674735092,953203371,379728005],

  [1070788282,363613908,401556515,737472501,916971534,741851784,
  15970839,575437740,308634173,456365136,610081937,655056737,
  566499647,146062168,11265212,228034960,802031966,1016657337,
  869981249,137320736,78544281,829883313,783146120,970701867,
  916026634,195792316,317440031,798963377,662445144,432575740],

  [512569269,413297986,617992871,699943554,930550099,360306596,
  942139075,636897660,837676953,680872486,958145976,99814098,
  1030494902,481157406,7043250,631984833,693125308,721326947,
  543308348,845963501,280625890,62529592,1069504905,437525669,
  15289504,1055367702,1030656218,1046177956,480251288,524111444],

  [992641068,539842223,236658812,663216381,130221500,781554959,
  707555422,697175772,211358555,98635777,101893269,685395385,
  212974975,754694168,348080315,797978796,610517654,353789515,
  740861326,561595503,738001445,148519155,1012540275,866018055,
  814844210,985429376,726145203,572582243,242483828,104550108],

  [1011761701,257012084,545603242,377614867,1001660721,374400720,
  330700341,414707616,712426496,517978447,955401637,627264514,
  163257057,560991681,704985699,647379336,71773275,710543791,
  1023151414,22605165,301433606,348091287,20570843,637748854,
  761625262,348250326,509470220,66005223,199807360,904227117],

  [30303575,619474536,775105061,606619342,1020249710,1007526750,
  1028531643,325064071,547200869,136261058,931704242,479402249,
  970006018,326468943,265514350,545747566,716265983,1066574193,
  925563822,652793902,970474175,832205384,982810047,1048889944,
  439489154,226597362,888136689,138618060,814046664,550833263]

  ],

  # DIMENSION dim=15,  generator matrices column encodings:

  [

  [122455510,773296462,80386005,883424770,513326595,981703937,
  1038812148,243570348,778200383,102755401,595654303,880576513,
  296182727,1055400600,996075111,1052355578,964134372,482021623,
  1010269190,146064639,699374654,545735549,783309448,241955223,
  391613045,316095920,691188546,107203704,913774004,919011693],

  [904829865,125800112,744836867,56211074,962495785,1014331605,
  31766538,1036440779,378917045,863948098,170171268,150539741,
  291559995,144340146,936281598,725120753,165033544,957473065,
  142516263,917214920,406122355,215612829,806188527,444563495,
  94075866,902187783,921358076,515829670,842057841,754580171],

  [144252053,719681002,764865240,360782177,8473587,170796252,
  322670896,824841090,715394417,308461745,767985005,603286018,
  282278856,370444133,799573691,207061925,378626792,443460925,
  747932389,190656701,112052892,838906526,456638239,308815925,
  314952227,615497055,197589208,851292505,114291449,749275465],

  [508763882,863822867,579200240,341866102,1020791415,952571345,
  739394084,867999885,527833410,840385800,558226716,581629303,
  539677350,61386309,344675504,571043943,679597514,131099271,
  983978597,401123019,825124467,1023625675,887540408,932091587,
  134304604,538330537,662740073,203901635,988267545,346153028],

  [621391692,190216341,240288833,47344896,848418599,660064937,
  724208392,17567804,947270235,290260854,65728614,661215123,
  409991240,708141568,308244599,200143731,276033077,525109062,
  395293500,464968947,618144500,326508566,615516113,557986837,
  45672459,435884540,701004880,63546760,785500141,862516802],

  [943528403,7424764,444055955,410453694,92186155,283874613,
  17575750,133964545,995073250,957980469,277245753,188272488,
  587777482,95089141,581464409,824556694,437316241,640484097,
  696373407,412102094,239622123,522038752,228604636,453088305,
  1071365639,498667903,869393790,449562132,1033358097,817761061],

  [1023859687,860420336,437777716,959192061,251318774,343778092,
  413416680,259452981,676804407,122487975,95708507,1054678216,
  363422616,466995666,325488046,373888941,515222328,781087025,
  997868815,459829544,41014936,226257344,331113322,597700410,
  963882199,450825004,1020970018,804124363,40896571,505564148],

  [755137672,742859173,936475141,354522321,797948600,730638890,
  204492398,159152738,471715321,123471289,839297694,642348689,
  750583992,76497646,744562819,577560611,139554140,626389783,
  521865008,377281746,344637867,286741651,324330987,196287246,
  804548810,417370381,309802854,984272094,97243419,1025617989],

  [510369304,236761812,13110549,616873707,521953617,792634244,
  531230079,775306128,407484179,747791618,694386176,331508215,
  818343003,781023012,308300789,805796298,944521705,592032883,
  269937303,405771211,145315315,973429799,145186174,1009885150,
  723080138,412171449,770686949,674735092,953203371,379728005],

  [1070788282,363613908,401556515,737472501,916971534,741851784,
  15970839,575437740,308634173,456365136,610081937,655056737,
  566499647,146062168,11265212,228034960,802031966,1016657337,
  869981249,137320736,78544281,829883313,783146120,970701867,
  916026634,195792316,317440031,798963377,662445144,432575740],

  [512569269,413297986,617992871,699943554,930550099,360306596,
  942139075,636897660,837676953,680872486,958145976,99814098,
  1030494902,481157406,7043250,631984833,693125308,721326947,
  543308348,845963501,280625890,62529592,1069504905,437525669,
  15289504,1055367702,1030656218,1046177956,480251288,524111444],

  [992641068,539842223,236658812,663216381,130221500,781554959,
  707555422,697175772,211358555,98635777,101893269,685395385,
  212974975,754694168,348080315,797978796,610517654,353789515,
  740861326,561595503,738001445,148519155,1012540275,866018055,
  814844210,985429376,726145203,572582243,242483828,104550108],

  [1011761701,257012084,545603242,377614867,1001660721,374400720,
  330700341,414707616,712426496,517978447,955401637,627264514,
  163257057,560991681,704985699,647379336,71773275,710543791,
  1023151414,22605165,301433606,348091287,20570843,637748854,
  761625262,348250326,509470220,66005223,199807360,904227117],

  [30303575,619474536,775105061,606619342,1020249710,1007526750,
  1028531643,325064071,547200869,136261058,931704242,479402249,
  970006018,326468943,265514350,545747566,716265983,1066574193,
  925563822,652793902,970474175,832205384,982810047,1048889944,
  439489154,226597362,888136689,138618060,814046664,550833263],

  [342919228,684064825,70595553,821444772,1067772687,228365088,
  875508409,523521168,568857749,27801078,14205486,54170645,
  762348034,442111606,779018993,91884115,96334799,834145058,
  517198826,311189041,351655502,129132263,71651785,69478110,
  877457343,69399165,663085682,432724522,901588315,1036418771]

  ],

  # DIMENSION dim=16,  generator matrices column encodings:

  [

  [122028500,773796640,79828983,881800358,514905835,983783335,
  1036076530,244094596,778726717,102223501,595753535,877977665,
  293940545,1052797592,998015535,1049706940,961932202,479425179,
  1008703202,146074807,699208338,545769971,783872744,241400761,
  394095793,318234454,691017632,107693692,912226258,921650147],

  [905747129,125669856,745948482,56213465,962367329,1013342451,
  33005913,1037353434,377933797,863814511,170368760,150537961,
  291553302,143356869,937198823,724066463,163851778,956426595,
  141337432,918194684,406318084,215609507,806253540,443391870,
  94009789,903116998,921416576,514601025,842089657,754668748],

  [144510343,719814161,764739186,360776817,8475867,170405149,
  322931744,825103235,715522888,308466584,767859270,603415209,
  282275890,370575710,799840954,206934734,378632555,443071164,
  748066014,190526844,111925134,838907447,456500383,309079437,
  315082098,615099103,197455650,851153078,113882241,749580267],

  [508694523,864018879,579267946,342582253,1020795729,953030849,
  739794289,867481205,527701809,840844607,558748283,581697196,
  539742130,61383864,344610789,571041724,679594220,131096939,
  983843120,400800768,824994954,1023559165,888130186,931957442,
  134307115,538930046,662758996,203788510,988761297,346276074],

  [621389988,190147614,240354817,47413693,849070421,659871401,
  724277355,17702764,947205554,289740834,65137593,660818834,
  409403056,708667867,308049550,199617242,275965133,524584535,
  395099063,465555703,618149148,326449146,616170625,558444702,
  45281988,435823313,700583419,63138695,785407875,862058847],

  [1024840886,860416911,437581387,960368629,251385071,342867483,
  414589371,259388234,675558717,122625022,95841389,1054808264,
  363428799,466082259,325425371,374938769,514306939,782072930,
  997935942,459831567,39967148,226387339,331250224,597702156,
  963817961,450635098,1021034056,805254254,39948930,505476103],

  [943528130,6377416,442877338,409279699,92188770,283745105,
  18625358,132919617,995069163,957055041,278160177,187351096,
  588960203,94958252,582645249,825737187,437319588,640489793,
  696376298,411055566,240803234,520987896,228602589,454136105,
  1070180458,498802178,868346947,449441731,1033212799,816755189],

  [755131930,742733924,936471700,354519697,797680387,730378704,
  204496645,158891697,471453056,123212969,839163918,642739562,
  750322088,76238277,744564601,577303792,139553741,626517950,
  522000409,377015466,344773034,286611154,324463697,196282908,
  804678176,417369934,309669814,984410809,97361422,1025588420],

  [509774441,236305777,13111597,617457706,521501292,792079340,
  530609804,775923580,406928336,748418988,694905554,332067769,
  818309335,780466121,308368901,805729970,943997647,591997436,
  270497271,405771136,144758335,973980081,145641057,1009847578,
  723049798,412204818,770093665,675196944,953790072,380349499],

  [1071829370,363611179,400021605,737468978,915884092,739197071,
  12782863,578052546,308135759,453717337,611167682,655090680,
  570175856,143441666,10178396,228528946,804652632,1016134480,
  869977617,137349722,78541999,829917227,782058450,971718430,
  916580062,195768456,316897570,799508767,662448934,435202045],

  [514439921,411228727,618086450,697847559,930424358,358576228,
  942010818,636808815,835672190,682739891,958268136,99823447,
  1028538355,480855611,7031412,632123921,693133855,721035685,
  543473531,843998686,278569684,62554824,1067281322,439356997,
  13233123,1053001636,1028403740,1046301216,480255387,524286967],

  [992744004,539739079,236795785,663216675,130224767,781522855,
  707424299,696815199,211785248,98668673,101863869,685563385,
  212940913,754823102,347687424,797980002,610518958,353825990,
  741254507,562021180,737903974,148684693,1012708501,865658034,
  814815730,985298406,726535512,572583637,242483404,104681103],

  [410584653,1014456740,859507316,528229087,21041245,451335112,
  273376174,370447156,145225655,100856626,216137927,880988295,
  989591832,498229517,752029644,692203068,378212597,210534553,
  1006542675,571190962,414912293,605262338,705870606,973888734,
  652138388,898974866,574612904,349338863,639882306,1002077865],

  [1011833690,256942639,546060759,378076728,1002288904,374437599,
  331255010,414611228,713020731,517449415,955993684,627269219,
  163250620,561092153,705439834,647441968,71777603,710053662,
  1023152908,22606250,301863081,347532963,20017716,637718071,
  761555051,348747465,509441421,65484519,199315376,904785068],

  [342919423,684098882,70628500,821483431,1067777746,228200923,
  875147916,523525120,569279558,28225579,14565382,54301638,
  762352194,442241525,778625199,92020179,96204354,834571042,
  517199569,311086769,351618653,129164929,71684553,69476856,
  877292194,69366427,663054204,432857041,901460654,1036450973],

  [32268518,619642010,775359809,604787067,1020096905,1009492987,
  1030488316,323225398,549425125,136161349,934053943,479673465,
  972140115,324513836,267614303,547742461,716557290,1068906183,
  925792527,650693947,972834248,834331210,982702238,1051098972,
  437684209,226568545,887965313,138875768,816273500,553069006]

  ],


  # DIMENSION dim=17,  generator matrices column encodings:

  [

  [129971866,403034142,42953265,456052922,529723536,39622889,
  1022405131,495125695,205765660,236811057,61590560,562939695,
  1009383060,28432675,166824630,956664215,988888538,657242377,
  1023579691,437431770,927205331,608312395,1072853475,655700129,
  27075613,636512015,837235128,226005552,875432949,795592105],

  [240208052,897491798,957022978,171139102,93849129,244950800,
  344159584,111102217,678504858,574516126,250455084,391388795,
  133277104,489333922,140361892,410735402,619253688,1031862789,
  335691611,322432037,806111734,694909702,349940897,602532064,
  148117500,111729200,457404274,557714256,1040149279,403498667],

  [432640305,1037156381,314925778,372080644,940221914,572058354,
  1038338338,426569089,455769817,491120620,1057021567,302721707,
  246475132,705152316,499194294,113265561,426137972,136848280,
  562415570,787892679,852991603,351729970,96778882,304416578,
  86282104,1036217109,157944466,954042255,414571869,870959303],

  [971287756,89414420,204713973,378635447,401797896,163681059,
  751966264,537449399,801535112,1071633688,146052774,3986810,
  636727079,697417592,1006763522,383199535,663223922,144535570,
  201016558,746200892,854342532,328874258,155896922,499850531,
  936254650,7138453,1071466390,61395452,636873816,304460150],

  [328557410,777876265,101075537,435479976,525041988,303555745,
  350113747,339410275,684034311,889925340,401693876,1060788096,
  113705201,1015366269,1065286982,10076601,952361191,167950482,
  435129959,233185538,781449455,798849169,428671146,124812670,
  188788880,15299783,859915815,1015278018,326831435,1018648256],

  [754655229,72701120,953293325,631599840,89857942,554011778,
  47073811,835760886,265073629,127620500,308658367,867391607,
  203498672,894076239,524964741,312496838,313578784,269715110,
  705844852,823949536,1027242087,59395526,569377093,394836031,
  343701223,384460815,943904084,699855722,421835371,270791893],

  [745907108,944952526,82284004,699536358,361313725,905488055,
  1023155197,882057901,746645466,119817566,452638563,1550867,
  1031436690,776155790,394503730,685193551,228707474,911100838,
  964828725,508995720,1026359451,428405268,817946254,828929109,
  313584437,871581416,426427170,160301328,365965375,220499879],

  [1056914698,521647651,221143510,117107134,150943194,408928603,
  480271744,848194951,172435885,473080053,275662818,324152353,
  59283147,131089463,834982831,778766731,122554353,88292162,
  763906051,129869508,637389308,823280981,671656942,66520354,
  308342240,325794549,6816340,371091997,621547052,25705907],

  [352064385,40386260,880715911,677695864,1005975671,853795757,
  574407480,530348942,601261381,103248825,975989152,739827654,
  863177279,460530535,159413890,688421859,1044972575,795098007,
  801093227,1001062741,926378401,139434982,834760968,204950615,
  639313518,920958373,495164640,91682281,69551285,433426629],

  [830376956,810354778,986692688,439214662,955852394,611884049,
  928650736,168559105,1064592932,151376416,433454075,1011126901,
  608575983,128899860,905698379,606430135,179348441,821647220,
  998454680,127121984,795384066,600759059,199794554,295176814,
  939420101,914617710,1018471342,111811433,331709918,221179210],

  [425733878,658229029,912424615,386431078,862251738,293702507,
  1043902477,877189394,48926307,261568902,462823467,217704510,
  305034830,297130225,26429996,343060209,894475863,17832215,
  1065385292,231895796,449755847,855378457,567620577,152049881,
  814862897,582773843,514674944,282536321,434990576,459545057],

  [665803357,392676405,1034814418,748287515,958635983,4816387,
  1034522664,915407014,57358263,113520872,253432907,18329885,
  1870034,67039950,583108703,159185799,130709561,976056560,
  448806026,846991206,686503884,308824271,436305887,194443459,
  777220336,1039366896,793594637,928986568,632103016,946360556],

  [626519650,572986777,596911660,888597461,756498052,392128719,
  36970690,1052917571,313118633,522168466,842712620,894477415,
  1055471970,11136187,252204038,40861408,975737116,212304344,
  965813895,726672608,429270148,457534820,770940172,116146229,
  243261641,1010332968,788194608,944433533,826152594,747969338],

  [1071582690,774188573,739663870,52487898,1048372764,921959408,
  547457522,429672649,490994041,25062518,805601797,589439943,
  496185778,639115556,433359194,327519661,726063918,256775538,
  973277956,33829588,639364507,351093493,73945571,631973049,
  882014952,196800376,470141183,501641249,527537127,1041746568],

  [635515840,789421408,903280967,937233682,987061368,245651243,
  162035928,13403621,749035327,131961461,612384091,371767111,
  944735537,346467471,292218132,1012693329,199650456,41027984,
  707150170,430658317,13393404,392035786,595614074,557315511,
  666890400,868924491,243135067,323841161,1027036232,622805502],

  [449543741,1068764199,919033015,422588592,252659057,380512547,
  538163030,67298058,638240573,691740025,524238634,479950745,
  602605950,1001285057,908196893,633023435,307774415,725379120,
  956739667,806388387,886237605,205177588,348918954,334053401,
  738869676,213168145,1010252086,29197916,769372946,291583312],

  [741738850,1073019312,151484689,963933996,549606967,851354389,
  277323389,157310630,427601638,817151586,491424124,737041173,
  736095612,646603916,295404110,614293779,110322022,227217880,
  596496751,455560392,177091156,799938318,212552277,239995158,
  942974955,977308770,319620009,456207171,829064434,160328806]

  ],

  # DIMENSION dim=18,  generator matrices column encodings:

  [

  [129971866,403034142,42953265,456052922,529723536,39622889,
  1022405131,495125695,205765660,236811057,61590560,562939695,
  1009383060,28432675,166824630,956664215,988888538,657242377,
  1023579691,437431770,927205331,608312395,1072853475,655700129,
  27075613,636512015,837235128,226005552,875432949,795592105],

  [240208052,897491798,957022978,171139102,93849129,244950800,
  344159584,111102217,678504858,574516126,250455084,391388795,
  133277104,489333922,140361892,410735402,619253688,1031862789,
  335691611,322432037,806111734,694909702,349940897,602532064,
  148117500,111729200,457404274,557714256,1040149279,403498667],

  [432640305,1037156381,314925778,372080644,940221914,572058354,
  1038338338,426569089,455769817,491120620,1057021567,302721707,
  246475132,705152316,499194294,113265561,426137972,136848280,
  562415570,787892679,852991603,351729970,96778882,304416578,
  86282104,1036217109,157944466,954042255,414571869,870959303],

  [971287756,89414420,204713973,378635447,401797896,163681059,
  751966264,537449399,801535112,1071633688,146052774,3986810,
  636727079,697417592,1006763522,383199535,663223922,144535570,
  201016558,746200892,854342532,328874258,155896922,499850531,
  936254650,7138453,1071466390,61395452,636873816,304460150],

  [328557410,777876265,101075537,435479976,525041988,303555745,
  350113747,339410275,684034311,889925340,401693876,1060788096,
  113705201,1015366269,1065286982,10076601,952361191,167950482,
  435129959,233185538,781449455,798849169,428671146,124812670,
  188788880,15299783,859915815,1015278018,326831435,1018648256],

  [754655229,72701120,953293325,631599840,89857942,554011778,
  47073811,835760886,265073629,127620500,308658367,867391607,
  203498672,894076239,524964741,312496838,313578784,269715110,
  705844852,823949536,1027242087,59395526,569377093,394836031,
  343701223,384460815,943904084,699855722,421835371,270791893],

  [745907108,944952526,82284004,699536358,361313725,905488055,
  1023155197,882057901,746645466,119817566,452638563,1550867,
  1031436690,776155790,394503730,685193551,228707474,911100838,
  964828725,508995720,1026359451,428405268,817946254,828929109,
  313584437,871581416,426427170,160301328,365965375,220499879],

  [1056914698,521647651,221143510,117107134,150943194,408928603,
  480271744,848194951,172435885,473080053,275662818,324152353,
  59283147,131089463,834982831,778766731,122554353,88292162,
  763906051,129869508,637389308,823280981,671656942,66520354,
  308342240,325794549,6816340,371091997,621547052,25705907],

  [352064385,40386260,880715911,677695864,1005975671,853795757,
  574407480,530348942,601261381,103248825,975989152,739827654,
  863177279,460530535,159413890,688421859,1044972575,795098007,
  801093227,1001062741,926378401,139434982,834760968,204950615,
  639313518,920958373,495164640,91682281,69551285,433426629],

  [830376956,810354778,986692688,439214662,955852394,611884049,
  928650736,168559105,1064592932,151376416,433454075,1011126901,
  608575983,128899860,905698379,606430135,179348441,821647220,
  998454680,127121984,795384066,600759059,199794554,295176814,
  939420101,914617710,1018471342,111811433,331709918,221179210],

  [425733878,658229029,912424615,386431078,862251738,293702507,
  1043902477,877189394,48926307,261568902,462823467,217704510,
  305034830,297130225,26429996,343060209,894475863,17832215,
  1065385292,231895796,449755847,855378457,567620577,152049881,
  814862897,582773843,514674944,282536321,434990576,459545057],

  [665803357,392676405,1034814418,748287515,958635983,4816387,
  1034522664,915407014,57358263,113520872,253432907,18329885,
  1870034,67039950,583108703,159185799,130709561,976056560,
  448806026,846991206,686503884,308824271,436305887,194443459,
  777220336,1039366896,793594637,928986568,632103016,946360556],

  [626519650,572986777,596911660,888597461,756498052,392128719,
  36970690,1052917571,313118633,522168466,842712620,894477415,
  1055471970,11136187,252204038,40861408,975737116,212304344,
  965813895,726672608,429270148,457534820,770940172,116146229,
  243261641,1010332968,788194608,944433533,826152594,747969338],

  [1071582690,774188573,739663870,52487898,1048372764,921959408,
  547457522,429672649,490994041,25062518,805601797,589439943,
  496185778,639115556,433359194,327519661,726063918,256775538,
  973277956,33829588,639364507,351093493,73945571,631973049,
  882014952,196800376,470141183,501641249,527537127,1041746568],

  [635515840,789421408,903280967,937233682,987061368,245651243,
  162035928,13403621,749035327,131961461,612384091,371767111,
  944735537,346467471,292218132,1012693329,199650456,41027984,
  707150170,430658317,13393404,392035786,595614074,557315511,
  666890400,868924491,243135067,323841161,1027036232,622805502],

  [449543741,1068764199,919033015,422588592,252659057,380512547,
  538163030,67298058,638240573,691740025,524238634,479950745,
  602605950,1001285057,908196893,633023435,307774415,725379120,
  956739667,806388387,886237605,205177588,348918954,334053401,
  738869676,213168145,1010252086,29197916,769372946,291583312],

  [741738850,1073019312,151484689,963933996,549606967,851354389,
  277323389,157310630,427601638,817151586,491424124,737041173,
  736095612,646603916,295404110,614293779,110322022,227217880,
  596496751,455560392,177091156,799938318,212552277,239995158,
  942974955,977308770,319620009,456207171,829064434,160328806],

  [751747817,315669162,1072571913,627839530,710228931,164629564,
  195148759,354677796,438058535,197451362,893770061,655242823,
  933207855,1034931553,1008083539,186134820,228361620,632147422,
  1051983424,579762179,835229716,490118527,935155568,444896042,
  190533305,524870331,248465921,840689687,498889988,302936823]

  ],


  # DIMENSION dim=19,  generator matrices column encodings:

  [

  [129971866,403034142,42953265,456052922,529723536,39622889,
  1022405131,495125695,205765660,236811057,61590560,562939695,
  1009383060,28432675,166824630,956664215,988888538,657242377,
  1023579691,437431770,927205331,608312395,1072853475,655700129,
  27075613,636512015,837235128,226005552,875432949,795592105],

  [240208052,897491798,957022978,171139102,93849129,244950800,
  344159584,111102217,678504858,574516126,250455084,391388795,
  133277104,489333922,140361892,410735402,619253688,1031862789,
  335691611,322432037,806111734,694909702,349940897,602532064,
  148117500,111729200,457404274,557714256,1040149279,403498667],

  [432640305,1037156381,314925778,372080644,940221914,572058354,
  1038338338,426569089,455769817,491120620,1057021567,302721707,
  246475132,705152316,499194294,113265561,426137972,136848280,
  562415570,787892679,852991603,351729970,96778882,304416578,
  86282104,1036217109,157944466,954042255,414571869,870959303],

  [971287756,89414420,204713973,378635447,401797896,163681059,
  751966264,537449399,801535112,1071633688,146052774,3986810,
  636727079,697417592,1006763522,383199535,663223922,144535570,
  201016558,746200892,854342532,328874258,155896922,499850531,
  936254650,7138453,1071466390,61395452,636873816,304460150],

  [328557410,777876265,101075537,435479976,525041988,303555745,
  350113747,339410275,684034311,889925340,401693876,1060788096,
  113705201,1015366269,1065286982,10076601,952361191,167950482,
  435129959,233185538,781449455,798849169,428671146,124812670,
  188788880,15299783,859915815,1015278018,326831435,1018648256],

  [754655229,72701120,953293325,631599840,89857942,554011778,
  47073811,835760886,265073629,127620500,308658367,867391607,
  203498672,894076239,524964741,312496838,313578784,269715110,
  705844852,823949536,1027242087,59395526,569377093,394836031,
  343701223,384460815,943904084,699855722,421835371,270791893],

  [745907108,944952526,82284004,699536358,361313725,905488055,
  1023155197,882057901,746645466,119817566,452638563,1550867,
  1031436690,776155790,394503730,685193551,228707474,911100838,
  964828725,508995720,1026359451,428405268,817946254,828929109,
  313584437,871581416,426427170,160301328,365965375,220499879],

  [1056914698,521647651,221143510,117107134,150943194,408928603,
  480271744,848194951,172435885,473080053,275662818,324152353,
  59283147,131089463,834982831,778766731,122554353,88292162,
  763906051,129869508,637389308,823280981,671656942,66520354,
  308342240,325794549,6816340,371091997,621547052,25705907],

  [352064385,40386260,880715911,677695864,1005975671,853795757,
  574407480,530348942,601261381,103248825,975989152,739827654,
  863177279,460530535,159413890,688421859,1044972575,795098007,
  801093227,1001062741,926378401,139434982,834760968,204950615,
  639313518,920958373,495164640,91682281,69551285,433426629],

  [830376956,810354778,986692688,439214662,955852394,611884049,
  928650736,168559105,1064592932,151376416,433454075,1011126901,
  608575983,128899860,905698379,606430135,179348441,821647220,
  998454680,127121984,795384066,600759059,199794554,295176814,
  939420101,914617710,1018471342,111811433,331709918,221179210],

  [425733878,658229029,912424615,386431078,862251738,293702507,
  1043902477,877189394,48926307,261568902,462823467,217704510,
  305034830,297130225,26429996,343060209,894475863,17832215,
  1065385292,231895796,449755847,855378457,567620577,152049881,
  814862897,582773843,514674944,282536321,434990576,459545057],

  [665803357,392676405,1034814418,748287515,958635983,4816387,
  1034522664,915407014,57358263,113520872,253432907,18329885,
  1870034,67039950,583108703,159185799,130709561,976056560,
  448806026,846991206,686503884,308824271,436305887,194443459,
  777220336,1039366896,793594637,928986568,632103016,946360556],

  [626519650,572986777,596911660,888597461,756498052,392128719,
  36970690,1052917571,313118633,522168466,842712620,894477415,
  1055471970,11136187,252204038,40861408,975737116,212304344,
  965813895,726672608,429270148,457534820,770940172,116146229,
  243261641,1010332968,788194608,944433533,826152594,747969338],

  [1071582690,774188573,739663870,52487898,1048372764,921959408,
  547457522,429672649,490994041,25062518,805601797,589439943,
  496185778,639115556,433359194,327519661,726063918,256775538,
  973277956,33829588,639364507,351093493,73945571,631973049,
  882014952,196800376,470141183,501641249,527537127,1041746568],

  [635515840,789421408,903280967,937233682,987061368,245651243,
  162035928,13403621,749035327,131961461,612384091,371767111,
  944735537,346467471,292218132,1012693329,199650456,41027984,
  707150170,430658317,13393404,392035786,595614074,557315511,
  666890400,868924491,243135067,323841161,1027036232,622805502],

  [449543741,1068764199,919033015,422588592,252659057,380512547,
  538163030,67298058,638240573,691740025,524238634,479950745,
  602605950,1001285057,908196893,633023435,307774415,725379120,
  956739667,806388387,886237605,205177588,348918954,334053401,
  738869676,213168145,1010252086,29197916,769372946,291583312],

  [741738850,1073019312,151484689,963933996,549606967,851354389,
  277323389,157310630,427601638,817151586,491424124,737041173,
  736095612,646603916,295404110,614293779,110322022,227217880,
  596496751,455560392,177091156,799938318,212552277,239995158,
  942974955,977308770,319620009,456207171,829064434,160328806],

  [751747817,315669162,1072571913,627839530,710228931,164629564,
  195148759,354677796,438058535,197451362,893770061,655242823,
  933207855,1034931553,1008083539,186134820,228361620,632147422,
  1051983424,579762179,835229716,490118527,935155568,444896042,
  190533305,524870331,248465921,840689687,498889988,302936823],

  [231782923,564441136,313799900,266020321,107576271,637714276,
  276715238,1041069275,782157799,490431753,619629874,682769192,
  84396062,1057857132,297378685,291285635,788347610,651201612,
  634291722,566191297,848749961,222420643,105329531,619183894,
  916439463,89124187,439251173,359317962,570853204,769320185]

  ],

  # DIMENSION dim=20,  generator matrices column encodings:

  [

  [129971866,403034142,42953265,456052922,529723536,39622889,
  1022405131,495125695,205765660,236811057,61590560,562939695,
  1009383060,28432675,166824630,956664215,988888538,657242377,
  1023579691,437431770,927205331,608312395,1072853475,655700129,
  27075613,636512015,837235128,226005552,875432949,795592105],

  [240208052,897491798,957022978,171139102,93849129,244950800,
  344159584,111102217,678504858,574516126,250455084,391388795,
  133277104,489333922,140361892,410735402,619253688,1031862789,
  335691611,322432037,806111734,694909702,349940897,602532064,
  148117500,111729200,457404274,557714256,1040149279,403498667],

  [432640305,1037156381,314925778,372080644,940221914,572058354,
  1038338338,426569089,455769817,491120620,1057021567,302721707,
  246475132,705152316,499194294,113265561,426137972,136848280,
  562415570,787892679,852991603,351729970,96778882,304416578,
  86282104,1036217109,157944466,954042255,414571869,870959303],

  [971287756,89414420,204713973,378635447,401797896,163681059,
  751966264,537449399,801535112,1071633688,146052774,3986810,
  636727079,697417592,1006763522,383199535,663223922,144535570,
  201016558,746200892,854342532,328874258,155896922,499850531,
  936254650,7138453,1071466390,61395452,636873816,304460150],

  [328557410,777876265,101075537,435479976,525041988,303555745,
  350113747,339410275,684034311,889925340,401693876,1060788096,
  113705201,1015366269,1065286982,10076601,952361191,167950482,
  435129959,233185538,781449455,798849169,428671146,124812670,
  188788880,15299783,859915815,1015278018,326831435,1018648256],

  [754655229,72701120,953293325,631599840,89857942,554011778,
  47073811,835760886,265073629,127620500,308658367,867391607,
  203498672,894076239,524964741,312496838,313578784,269715110,
  705844852,823949536,1027242087,59395526,569377093,394836031,
  343701223,384460815,943904084,699855722,421835371,270791893],

  [745907108,944952526,82284004,699536358,361313725,905488055,
  1023155197,882057901,746645466,119817566,452638563,1550867,
  1031436690,776155790,394503730,685193551,228707474,911100838,
  964828725,508995720,1026359451,428405268,817946254,828929109,
  313584437,871581416,426427170,160301328,365965375,220499879],

  [1056914698,521647651,221143510,117107134,150943194,408928603,
  480271744,848194951,172435885,473080053,275662818,324152353,
  59283147,131089463,834982831,778766731,122554353,88292162,
  763906051,129869508,637389308,823280981,671656942,66520354,
  308342240,325794549,6816340,371091997,621547052,25705907],

  [352064385,40386260,880715911,677695864,1005975671,853795757,
  574407480,530348942,601261381,103248825,975989152,739827654,
  863177279,460530535,159413890,688421859,1044972575,795098007,
  801093227,1001062741,926378401,139434982,834760968,204950615,
  639313518,920958373,495164640,91682281,69551285,433426629],

  [830376956,810354778,986692688,439214662,955852394,611884049,
  928650736,168559105,1064592932,151376416,433454075,1011126901,
  608575983,128899860,905698379,606430135,179348441,821647220,
  998454680,127121984,795384066,600759059,199794554,295176814,
  939420101,914617710,1018471342,111811433,331709918,221179210],

  [425733878,658229029,912424615,386431078,862251738,293702507,
  1043902477,877189394,48926307,261568902,462823467,217704510,
  305034830,297130225,26429996,343060209,894475863,17832215,
  1065385292,231895796,449755847,855378457,567620577,152049881,
  814862897,582773843,514674944,282536321,434990576,459545057],

  [665803357,392676405,1034814418,748287515,958635983,4816387,
  1034522664,915407014,57358263,113520872,253432907,18329885,
  1870034,67039950,583108703,159185799,130709561,976056560,
  448806026,846991206,686503884,308824271,436305887,194443459,
  777220336,1039366896,793594637,928986568,632103016,946360556],

  [626519650,572986777,596911660,888597461,756498052,392128719,
  36970690,1052917571,313118633,522168466,842712620,894477415,
  1055471970,11136187,252204038,40861408,975737116,212304344,
  965813895,726672608,429270148,457534820,770940172,116146229,
  243261641,1010332968,788194608,944433533,826152594,747969338],

  [1071582690,774188573,739663870,52487898,1048372764,921959408,
  547457522,429672649,490994041,25062518,805601797,589439943,
  496185778,639115556,433359194,327519661,726063918,256775538,
  973277956,33829588,639364507,351093493,73945571,631973049,
  882014952,196800376,470141183,501641249,527537127,1041746568],

  [635515840,789421408,903280967,937233682,987061368,245651243,
  162035928,13403621,749035327,131961461,612384091,371767111,
  944735537,346467471,292218132,1012693329,199650456,41027984,
  707150170,430658317,13393404,392035786,595614074,557315511,
  666890400,868924491,243135067,323841161,1027036232,622805502],

  [449543741,1068764199,919033015,422588592,252659057,380512547,
  538163030,67298058,638240573,691740025,524238634,479950745,
  602605950,1001285057,908196893,633023435,307774415,725379120,
  956739667,806388387,886237605,205177588,348918954,334053401,
  738869676,213168145,1010252086,29197916,769372946,291583312],

  [741738850,1073019312,151484689,963933996,549606967,851354389,
  277323389,157310630,427601638,817151586,491424124,737041173,
  736095612,646603916,295404110,614293779,110322022,227217880,
  596496751,455560392,177091156,799938318,212552277,239995158,
  942974955,977308770,319620009,456207171,829064434,160328806],

  [751747817,315669162,1072571913,627839530,710228931,164629564,
  195148759,354677796,438058535,197451362,893770061,655242823,
  933207855,1034931553,1008083539,186134820,228361620,632147422,
  1051983424,579762179,835229716,490118527,935155568,444896042,
  190533305,524870331,248465921,840689687,498889988,302936823],

  [231782923,564441136,313799900,266020321,107576271,637714276,
  276715238,1041069275,782157799,490431753,619629874,682769192,
  84396062,1057857132,297378685,291285635,788347610,651201612,
  634291722,566191297,848749961,222420643,105329531,619183894,
  916439463,89124187,439251173,359317962,570853204,769320185],

  [676629042,890605142,1002839327,523688601,94150929,345382736,
  917470425,448046156,11104351,421774295,1003535548,690755745,
  1072393822,110502200,1046710617,863643895,501940838,1005596262,
  177889070,894474600,1024283517,536108296,511361182,597326621,
  33078708,897620545,435132721,213718759,160790581,74282284]

  ]
  
]
  

  
  return x
end

#nextPoint ⇒ Object

# File 'lib/NX.rb', line 42

def nextPoint()
  # find the position k of the rightmost zero bit of index
   # 0<=k<M
   k=0
   n=@index 
   x = Array.new(@dim)
  while (n%2 == 1)
    n=n>>1
    k=k+1
    #puts k
  end
  
  for j in 0..@dim-1
    @x_int[j]= @x_int[j] ^ @genMats[j][k]
    #puts @N.inspect
    x[j]=@x_int[j].to_f/@N.to_f
  end
@index =@index +1
return x
end

#restart ⇒ Object

The NX points

# File 'lib/NX.rb', line 37

def restart()
@index=1
  
end