Table for CAN(6,k,18) 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,18) 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 34012224 composition 8 38131351 Add a symbol 9 40374371 Add a symbol 10 42749334 Add a symbol 11 45264000 Add a symbol 20 47045879 orthogonal array fuse 21 86923493 Add a factor 22 126801107 Add a factor 24 148035879 orthogonal array fuse fuse fuse fuse fuse 25 188183465 perfect hash family4,25,19,c fuse 27 188183512 perfect hash family4,27,20 40 229452668 Martirosyan-Tran van Trung 41 323237690 Add a factor 42 423412775 perfect hash family9,42,19,c fuse 45 423412902 perfect hash family9,45,20 47 470458637 perfect hash family10,47,19,c fuse 51 470458780 perfect hash family10,51,20 53 517504499 perfect hash family11,53,19,c fuse 60 517504658 perfect hash family11,60,20 64 564550536 perfect hash family12,64,20 65 658642292 perfect hash family14,65,20 95 705687947 perfect hash family15,95,19,c fuse 96 705688170 perfect hash family15,96,20 133 739700393 Power 19^2T12 152 743819520 Power 19^2T11 171 746062540 Power 19^2T10 190 748437503 Power 19^2T9 209 750952169 Power 19^2T8 361 752733809 perfect hash family16,361,19,c fuse 362 752734048 Power 19^2+1 363 945827698 Add a factor 364 1146874900 Add a factor 366 1317284153 perfect hash family28,366,19,c fuse 368 1317284584 perfect hash family28,368,20 515 1505467601 perfect hash family32,515,19,c fuse 516 1505468096 perfect hash family32,516,20 517 1824051122 Add a factor 519 2070018632 perfect hash family44,519,20 520 2117063807 perfect hash family45,520,19,c fuse 522 2117064510 perfect hash family45,522,20 529 2368573869 perfect hash family16,529,23,c fuse fuse fuse fuse fuse 530 2368574048 Power 23^2+1 722 2448682933 Martirosyan-Tran van Trung 724 2484968004 Martirosyan-Tran van Trung 726 2781331758 Martirosyan-Tran van Trung 729 3010936176 Power 27^2 748 3171068135 Power N41^2T16S13 808 3171068182 Power N41^2T14S13 1194 3212337338 Power N41^2S14 1223 3306122360 Power N41^2S13 1253 3399907382 Power N41^2S12 1372 3441790005 Power N37^2+3 1381 3775047470 Power N41^2S8 1415 3868832492 Power N41^2S7 1450 3962617514 Power N41^2S6 1486 4056402536 Power N41^2S5 1523 4150187558 Power N41^2S4 1561 4243972580 Power N41^2S3 1600 4337757602 Power N41^2T1T1 1640 4431542624 Power N41^2T1 1681 4525327646 Power N41^2 1682 4979010284 Add a factor 1683 5432692922 Add a factor 1720 5733820380 Power N43^2T3 1722 5827605275 Power N43^2T2T1 1763 5827605402 Power N43^2T2 1764 5927780360 Power N43^2T1T1 1806 5927780487 Power N43^2T1 1851 5927780614 Power N43^2+2 1880 6345414935 Power N47^2T7 1927 6439199957 Power N47^2T6 2025 6492329434 Power N47^2T2T2 2115 6539375169 Power N47^2T2 2209 6586420904 Power N47^2 2212 6586422906 Power N47^2+3 2240 6730888899 Power 32^3T25T22 2304 6732633063 Power 32^3T24T23 2464 6733403565 Power 32^3T25T21 2592 6734876083 Power 32^3T23T23 4480 6735185444 Power 32^3T25T12 5120 6739304571 Power 32^3T24T12 5760 6741547591 Power 32^3T23T12 6400 6743922554 Power 32^3T22T12 7040 6746437220 Power 32^3T21T12 10000 6748219099 Power 31^3T11T11

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