Table for CAN(6,k,18) for k up to 10000

Last Updated Mon May 9 06:41:48 MST 2016

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 38120409 Augment OA 9 40346898 Augment OA 10 42690464 Augment OA 11 45151808 Augment OA 20 47045879 orthogonal array fuse 21 84448008 extended OA (Colbourn) special fuse 22 124325622 Add 1 factors 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 38 225325007 double OA (Colbourn-Zhou) fuse 40 227794247 double OA (Colbourn-Zhou) fuse 41 336759011 Add 1 factors 42 408043547 Add 2 factors 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 CT19^2T12 152 743808578 Power CT19^2T11 171 746035067 Power CT19^2T10 190 748378633 Power CT19^2T9 209 750839977 Power CT19^2T8 361 752733809 perfect hash family16,361,19,c fuse 362 752734048 Power CT19^2+1 363 945717538 Add 1 factors 364 1021259758 Add 2 factors 365 1124458024 Add 3 factors 366 1170231746 Add 5 factors 367 1170231985 Add 5 factors 368 1188881500 Add 6 factors 380 1228536179 Add 19 factors 381 1228536418 Add 19 factors 382 1425247906 Add 1 factors 383 1500790126 Add 2 factors 515 1505467601 perfect hash family32,515,19,c fuse 516 1505468096 perfect hash family32,516,20 517 1800176696 Add 1 factors 518 1928865608 Add 2 factors 519 2062610900 Add 3 factors 520 2094073283 Add 5 factors 521 2094073778 Add 5 factors 522 2117064510 perfect hash family45,522,20 524 2162121965 Add 19 factors 531 2164220819 Add 19 factors 533 2164344281 Add 19 factors 534 2169020447 Add 19 factors 535 2169020942 Add 19 factors 685 2220737084 Martirosyan-TVT variant 722 2221998414 Martirosyan-TVT 723 2230307459 Martirosyan-TVT variant 724 2238616265 Martirosyan-TVT 726 2502945185 Martirosyan-TVT 728 2642347157 Martirosyan-TVT 730 2795441171 Martirosyan-TVT 732 2859295583 Martirosyan-TVT 734 2862224701 Martirosyan-TVT 736 2907498137 Martirosyan-TVT 741 2908617450 Add 19 factors 742 2916926495 Add 19 factors 743 2929401887 Add 19 factors 760 2947152816 Martirosyan-TVT 761 2951791337 Martirosyan-TVT variant 762 2956429619 Martirosyan-TVT 808 3149508709 Power N-CT41^2T14S13 1134 3186650204 Power N-CT41^2T3S13 1198 3189119444 Power N-CT41^2Arc(14) 1226 3298084208 Power N-CT41^2Arc(13) 1370 3379875090 Power N-CT37^2+1 1372 3416913690 Power N-CT37^2+3 1373 3815910762 Add 1 factors 1381 3842908028 Power N-CT41^2Arc(8) 1415 3951872792 Power N-CT41^2Arc(7) 1450 4060837556 Power N-CT41^2Arc(6) 1486 4169802320 Power N-CT41^2Arc(5) 1523 4278767084 Power N-CT41^2Arc(4) 1561 4387731848 Power N-CT41^2Arc(3) 1600 4496696612 Power N-CT41^2T1T1 1640 4605661376 Power N-CT41^2T1 1681 4714626140 Power N-CT41^2 1682 5118489836 Add 1 factors 1683 5291083016 Add 2 factors 1684 5464988738 Add 3 factors 1686 5482955183 Add 5 factors 1687 5515316201 Add 6 factors 1700 5576416892 Add 19 factors 1720 5732161959 Power N-CT43^2T3 1722 5825757368 Power N-CT43^2T2T1 1763 5841126723 Power N-CT43^2T2 1764 5897041904 Power N-CT43^2T1T1 1806 5912411259 Power N-CT43^2T1 1851 5927780614 Power N-CT43^2+2 1852 6334542436 Add 1 factors 1880 6343756514 Power N-CT47^2T7 2800 6437204147 Power CT31^3T24T11T11 3200 6441312332 Power CT31^3T23T11T11 3600 6443538821 Power CT31^3T22T11T11 4000 6445882387 Power CT31^3T21T11T11 4400 6448343731 Power CT31^3T20T11T11 8000 6450237802 Power CT31^3T11T11T11 8400 6487639931 Power CT31^3T11T11T10 8820 6525042060 Power CT31^3T11T10T10 9600 6551227802 Power CT31^3T11T11T7 10000 6588629931 Power CT31^3T11T10T7

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