Table for CAN(6,k,15) for k up to 10000

Last Updated Sun Nov 22 06:45:17 MST 2009

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,15) 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 7 11390625 composition 8 15165027 Add a symbol 17 16777214 orthogonal array fuse 18 24137565 orthogonal array fuse fuse 19 37899705 Add a factor 20 47045873 orthogonal array fuse fuse fuse fuse 21 67108814 perfect hash family4,21,16,c fuse 23 67108852 perfect hash family4,23,17 34 81321023 Martirosyan-Tran van Trung 36 103312746 Martirosyan-Tran van Trung 37 143687766 Add a factor 39 167772130 perfect hash family10,39,17 40 184549214 perfect hash family11,40,16,c fuse 44 184549343 perfect hash family11,44,17 50 201326556 perfect hash family12,50,17 53 218103769 perfect hash family13,53,17 60 234880982 perfect hash family14,60,17 80 251658014 perfect hash family15,80,16,c fuse 85 251658195 Power 17^2Tlev 119 263048819 Power 17^2T10 136 266823221 Power 17^2T9 256 268435214 perfect hash family16,256,16,c fuse 289 268435408 Power 17^2 290 340862728 Add a factor 291 425463538 Add a factor 292 469761964 perfect hash family28,292,17 293 520093603 perfect hash family31,293,17 512 536870414 perfect hash family32,512,16,c fuse 513 536870816 perfect hash family32,513,17 514 646755626 Add a factor 516 754974585 perfect hash family45,516,17 517 864859395 Add a factor 544 881860817 Martirosyan-Tran van Trung 576 917854683 Martirosyan-Tran van Trung 578 978417308 perfect hash familyD16,578,34^11 17^5 579 1116086588 Add a factor 580 1122422649 Martirosyan-Tran van Trung 589 1176394012 Power N31^2T12 620 1185540180 Power N31^2T11 651 1205603121 Power N31^2T10 713 1205603159 Power N31^2T8 964 1219815330 Power N31^2+3 1026 1301136352 Power 32^2+2 1027 1456125592 Add a factor 1028 1611114832 Add a factor 1044 1751566275 Power N37^2S10 1072 1791941295 Power N37^2S9 1101 1832316315 Power N37^2S8 1131 1872691335 Power N37^2S7 1162 1913066355 Power N37^2S6 1194 1953441375 Power N37^2S5 1227 1993816395 Power N37^2S4 1261 2034191415 Power N37^2S3 1296 2074566435 Power N37^2T1T1 1332 2114941455 Power N37^2T1 1425 2147483264 perfect hash family128,1425,17 1426 2302472504 Add a factor 1428 2365587033 perfect hash family141,1428,17 1568 2381090886 Power 32^3T25T25 1792 2384865288 Power 32^3T25T24 3808 2386477475 Power 32^3T25T15 4352 2390251877 Power 32^3T24T15 9248 2391864064 Power 32^3T15T15 9792 2399224415 Power 32^3T15T14 10000 2406584766 Power 31^3T13T13

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