Table for CAN(6,k,13) for k up to 10000

Last Updated Tue Jan 31 05:20:10 MST 2012

Locate the k in the first column that is at least as large as the number of factors in which you are interested. Then let N be the number of rows (tests) given in the second column. A CA(N;6,k,13) exists according to a construction in the reference (cryptically) given in the third column. The accompanying graph plots N vertically against log k (base 10).

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k N Source 14 4826809 orthogonal array 15 9253764 extended OA (Colbourn) 16 13709280 Add a factor 17 16777210 orthogonal array fuse fuse fuse 18 19307232 perfect hash family4,18,14 26 22648873 double OA (Colbourn-Zhou) 28 23017969 double OA (Colbourn-Zhou) 29 34169941 Add a factor 30 47165521 Add a factor 32 53094888 perfect hash family11,32,14 34 57921696 perfect hash family12,34,14 37 62748504 perfect hash family13,37,14 40 67575312 perfect hash family14,40,14 43 72402120 perfect hash family15,43,14 65 77228749 perfect hash family16,65,13,c 66 77228928 perfect hash family16,66,14 67 98451948 Add a factor 68 106189776 perfect hash family22,68,14 69 111016321 perfect hash family23,69,13,c 70 111016584 perfect hash family23,70,14 71 121898331 perfect hash family17,120,15S8 76 126325286 perfect hash family17,120,15S7 81 130752241 perfect hash family17,120,15S6 86 135179196 perfect hash family17,120,15S5 112 139406225 Power CT16^2Arc(18):9 twos,0 ones 120 148060208 Power CT16^2Arc(16) 121 152515724 Power CT16^2Arc(15) 123 156971240 Power CT16^2Arc(14) 126 161426756 Power CT16^2Arc(13) 130 165882272 Power CT16^2Arc(12) 135 170337788 Power CT16^2Arc(11) 141 174793304 Power CT16^2Arc(10) 148 179248820 Power CT16^2Arc(9) 156 183704336 Power CT16^2Arc(8) 165 188159852 Power CT16^2Arc(7) 175 192615368 Power CT16^2Arc(6) 186 197070884 Power CT16^2Arc(5) 198 201526400 Power CT16^2Arc(4) 211 205981916 Power CT16^2Arc(3) 225 210437432 Power CT16^2T1T1 240 214892948 Power CT16^2T1 256 219348464 Power CT16^2 257 251035964 Add a factor 272 265367414 Power CT17^2T1 289 268435344 Power CT17^2 290 301071948 Add a factor 291 333708552 Add a factor 308 339028761 Power N-CT29^2T12S14 325 341558783 Power N-CT29^2T11S14 350 344559888 Power CT25^2T11 466 344900424 Power N-CT29^2T3S14 511 345269520 Power N-CT29^2Arc(15) 526 356421492 Power N-CT29^2Arc(14) 626 362381952 Power CT25^2+1 627 366811104 Power CT27^2Arc(4) 651 367180200 Power CT27^2Arc(3) 676 367549296 Power CT27^2T1T1 702 367918392 Power CT27^2T1 730 368287488 Power CT27^2+1 731 414162876 Add a factor 732 460038264 Add a factor 757 479093184 Power N-CT29^2Arc(3) 784 490245156 Power N-CT29^2T1T1 812 501397128 Power N-CT29^2T1 841 512549100 Power N-CT29^2 842 561928872 Add a factor 843 611308644 Add a factor 844 660688416 Add a factor 845 710068188 Add a factor 846 759447960 Add a factor 868 766346386 Power N-CT31^2T3 870 771568991 Power N-CT31^2T2T1 899 777498358 Power N-CT31^2T2 900 784564571 Power N-CT31^2T1T1 930 790493938 Power N-CT31^2T1 962 796423305 Power N-CT31^2+1 1004 813266711 Martirosyan-Tran van Trung 1008 813434879 Martirosyan-Tran van Trung 1014 813450167 Martirosyan-Tran van Trung 1022 829882727 Martirosyan-Tran van Trung 1040 845595099 Martirosyan-Tran van Trung 1052 845887131 Martirosyan-Tran van Trung 1060 851847591 Martirosyan-Tran van Trung 1064 852000471 Martirosyan-Tran van Trung 1092 852031047 Martirosyan-Tran van Trung 1116 861027255 Martirosyan-Tran van Trung 1120 861042543 Martirosyan-Tran van Trung 1128 861118983 Martirosyan-Tran van Trung 1144 861210711 Martirosyan-Tran van Trung 1172 861502743 Martirosyan-Tran van Trung 1192 861548607 Martirosyan-Tran van Trung 1196 861594471 Martirosyan-Tran van Trung 1216 861886503 Martirosyan-Tran van Trung 1232 861932367 Martirosyan-Tran van Trung 1248 861978231 Martirosyan-Tran van Trung 1252 864340695 Martirosyan-Tran van Trung 1254 868769847 Martirosyan-Tran van Trung 1292 869138943 Martirosyan-Tran van Trung 1302 869245959 Martirosyan-Tran van Trung 1328 869615055 Martirosyan-Tran van Trung 1352 869691495 Martirosyan-Tran van Trung 1360 872106243 Martirosyan-Tran van Trung 1404 879763659 Martirosyan-Tran van Trung 1460 880132755 Martirosyan-Tran van Trung 1461 929512527 Add a factor 1462 945306591 Martirosyan-Tran van Trung 1486 989495626 Power N-CT41^2Arc(5) 1523 994322434 Power N-CT41^2Arc(4) 1561 999149242 Power N-CT41^2Arc(3) 1600 1003976050 Power N-CT41^2T1T1 1720 1008802858 Power N-CT43^2T3 1849 1013629666 Power N-CT43^2 1952 1057068611 Power N-CT61^2T29 2074 1061895419 Power N-CT61^2T27 2257 1066722227 Power N-CT61^2T24 2440 1071549035 Power N-CT61^2T21 2623 1076375843 Power N-CT61^2T18 3724 1081202472 Power N-CT61^2+3 3751 1123651018 Power N-CT67^2Arc(12) 3807 1144874038 Power N-CT67^2Arc(11) 3864 1166097058 Power N-CT67^2Arc(10) 3922 1187320078 Power N-CT67^2Arc(9) 3981 1208543098 Power N-CT67^2Arc(8) 4041 1229766118 Power N-CT67^2Arc(7) 4097 1235659789 perfect hash family256,4097,13,c 4098 1235662832 Power CT64^2+2 4102 1250989138 Power N-CT67^2Arc(6) 4164 1272212158 Power N-CT67^2Arc(5) 4227 1293435178 Power N-CT67^2Arc(4) 4291 1314658198 Power N-CT67^2Arc(3) 4356 1335881218 Power N-CT67^2T1T1 4422 1357104238 Power N-CT67^2T1 4489 1378327258 Power N-CT67^2 5040 1419792408 Power CT31^3T17S30 5400 1424219363 Power CT31^3T16S30 5758 1428674879 Power CT31^3T15S30 6119 1431742809 Power CT31^3T14S30 6477 1434272831 Power CT31^3T13S30 9351 1437614472 Power CT31^3T5S30 10000 1437983568 Power CT31^3T3S30

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