Table for CAN(6,k,17) for k up to 10000

Last Updated Sat Nov 16 19:19:53 MST 2019

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,17) 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 18 24137569 orthogonal array 19 46771760 extended OA (Colbourn) 20 47045877 orthogonal array fuse fuse 23 70992833 5-Restricted SCPHF RE (CL) 25 72329169 4-Restricted SCPHF RE (CL) 27 72412673 SCPHF Random Extension (CLS) 35 93710545 5,5-Restricted SCPHF RE (CL) 38 95130385 5-Restricted SCPHF RE (CL) 41 96466721 4-Restricted SCPHF RE (CL) 42 96550225 SCPHF Random Extension (CLS) 53 117848097 5,5-Restricted SCPHF RE (CL) 57 119267937 5-Restricted SCPHF RE (CL) 62 120604273 4-Restricted SCPHF RE (CL) 65 120682881 3-Restricted SCPHF RE (CL) 66 120687777 SCPHF Random Extension (CLS) 77 140565809 5,5,5-Restricted SCPHF RE (CL) 86 141985649 5,5-Restricted SCPHF RE (CL) 96 143405489 5-Restricted SCPHF RE (CL) 105 144741825 4-Restricted SCPHF RE (CL) 106 144820433 3-Restricted SCPHF RE (CL) 108 144825057 2-Restricted SCPHF RE (CL) 125 164703361 5,5,5-Restricted SCPHF RE (CL) 139 166123201 5,5-Restricted SCPHF RE (CL) 156 167543041 5-Restricted SCPHF RE (CL) 167 168879377 4-Restricted SCPHF RE (CL) 171 168957985 3-Restricted SCPHF RE (CL) 176 168962609 2-Restricted SCPHF RE (CL) 177 168962881 SCPHF Random Extension (CLS) 178 168962977 CPHF Random Extension (CLS) 268 193100433 SCPHF Random Extension (CLS) 269 302601377 Add 1 factors 270 347958193 Add 2 factors 289 386200849 perfect hash family16,289,17,c 290 386201088 Power CT17^2+1 291 495702032 Add 1 factors 292 541132832 Add 2 factors 293 585231920 Add 3 factors 294 607949632 Add 4 factors 306 630667105 Add 17 factors 307 630667344 Add 17 factors 324 703079762 Power CT19^2T1T1 342 725713953 Power CT19^2T1 361 748348144 Power CT19^2 362 752734016 Power CT19^2+1 513 772401681 perfect hash family32,513,17,c 514 772402176 perfect hash family32,514,18 536 896022468 Martirosyan-TVT 620 965502160 perfect hash family5,620,268 621 1100379616 Add 1 factors 625 1157266688 Power CT25^2 675 1158519248 Power CT27^2T2 754 1158602592 perfect hash family6,754,268 755 1294737776 Add 1 factors 760 1299776900 Power N-CT41^2T21T3 779 1300839119 Power N-CT41^2T22 820 1301113236 Power N-CT41^2T21 882 1322387520 Power N-CT41^2Trin3,6,14 945 1323723856 Power N-CT41^2T14T6 954 1323807360 Power N-CT41^2Trin3,3,14 1026 1325143696 Power N-CT41^2T14T3 1107 1326480032 Power N-CT41^2T14 1138 1343685392 Power N-CT41^2Trin3,6,6 1225 1345021728 Power N-CT41^2T6T6 1234 1345105232 Power N-CT41^2Trin3,3,6 1330 1346441568 Power N-CT41^2T6T3 1339 1346525072 Power N-CT41^2Trin3,3,3 1435 1347777904 Power N-CT41^2T6 1444 1347861408 Power N-CT41^2T3T3 1558 1349197744 Power N-CT41^2T3 1681 1350534080 Power N-CT41^2 1682 1351703136 Power N-CT41^2+1 1683 1510699376 Add 1 factors 1723 1585979728 Power N-CT43^2Arc(3) 1764 1607277600 Power N-CT43^2T1T1 1855 1625735792 Power N-CT53^2T18 2014 1627155632 Power N-CT53^2T15 2173 1628491968 Power N-CT53^2T12 2226 1628575472 Power N-CT53^2T11 2809 1649873344 Power N-CT53^2 2813 1669751104 perfect hash family14,2813,57 2919 1683030960 Power N-CT59^2Trin2,2,6 3021 1684367296 Power N-CT59^2T6T2 3139 1684450800 Power N-CT59^2Trin2,2,2 3233 1685703632 Power N-CT61^2T8 3249 1685787136 Power N-CT59^2T2T2 3477 1687123472 Power N-CT61^2T4 3722 1688459808 Power N-CT61^2+1 3725 1689560320 perfect hash family14,3725,65 3726 1689628864 perfect hash family14,3726,66 3751 1729384928 Power N-CT67^2Arc(12) 3807 1749262960 Power N-CT67^2Arc(11) 3826 1767711616 Power N-CT73^2Trin7,8,8 3884 1767716512 Power N-CT73^2Trin7,7,8 3943 1767721408 Power N-CT73^2Trin7,7,7 4030 1787511040 Power N-CT73^2T11T8 4092 1787515936 Power N-CT73^2T11T7 4225 1787589648 Power N-CT73^2T8T8 4290 1787594544 Power N-CT73^2T8T7 4356 1787599440 Power N-CT73^2T7T7 4526 1807393968 Power N-CT73^2T11 4745 1807472576 Power N-CT73^2T8 4818 1807477472 Power N-CT73^2T7 4879 1821670976 Power N-CT79^2Trin2,2,14 4954 1821675872 Power N-CT79^2Trin2,2,13 5005 1823090816 Power N-CT79^2T14T2 5082 1823095712 Power N-CT79^2T13T2 5146 1824432048 Power N-CT83^2T21 5395 1824510656 Power N-CT83^2T18 5478 1824515552 Power N-CT83^2T17 5487 1838713952 Power N-CT89^2Trin3,3,23 5590 1840128896 Power N-CT89^2T24T3 5676 1840133792 Power N-CT89^2T23T3 5785 1841548736 Power N-CT89^2T24 5874 1841553632 Power N-CT89^2T23 5929 1842973744 Power N-CT79^2T2T2 6391 1844393584 Power N-CT83^2T6 6892 1845813424 Power N-CT83^2+3 6955 1858583552 perfect hash family13,11449,107T42 7062 1858588448 perfect hash family13,11449,107T41 7147 1860011824 Power N-CT89^2Trin3,3,3 7396 1861431664 Power N-CT89^2T3T3 7654 1862851504 Power N-CT89^2T3 8058 1862935008 Power N-CT97^2Arc(13)T2 8226 1864271344 Power N-CT97^2Arc(13) 8311 1865607680 Power N-CT97^2Arc(12) 8397 1866944016 Power N-CT97^2Arc(11) 8484 1868280352 Power N-CT97^2Arc(10) 8572 1869616688 Power N-CT97^2Arc(9) 8661 1870953024 Power N-CT97^2Arc(8) 8751 1872289360 Power N-CT97^2Arc(7) 8842 1873625696 Power N-CT97^2Arc(6) 8934 1874962032 Power N-CT97^2Arc(5) 9027 1876298368 Power N-CT97^2Arc(4) 9121 1877634704 Power N-CT97^2Arc(3) 9216 1878971040 Power N-CT97^2T1T1 9888 1880307376 perfect hash family13,10609,103T7 10000 1881306160 perfect hash family13,11449,107T11

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