Table for CAN(6,k,15) 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,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 15080613 Augment OA 17 16777214 orthogonal array fuse 18 24137565 orthogonal array fuse fuse 19 37899705 Add 1 factors 20 47045873 orthogonal array fuse fuse fuse fuse 22 49283054 5-Restricted SCPHF RE (CL) fuse 25 50266094 4-Restricted SCPHF RE (CL) fuse 26 50331614 SCPHF Random Extension (CLS) fuse 33 65011694 5,5-Restricted SCPHF RE (CL) fuse 35 66060254 5-Restricted SCPHF RE (CL) fuse 39 67043294 4-Restricted SCPHF RE (CL) fuse 40 67108814 SCPHF Random Extension (CLS) fuse 41 67108859 CPHF Random Extension (CLS) fuse 51 81788894 5,5-Restricted SCPHF RE (CL) fuse 56 82837454 5-Restricted SCPHF RE (CL) fuse 58 83820494 4-Restricted SCPHF RE (CL) fuse 63 83881934 3-Restricted SCPHF RE (CL) fuse 64 83885774 2-Restricted SCPHF RE (CL) fuse 66 83886014 SCPHF Random Extension (CLS) fuse 73 97517534 5,5,5-Restricted SCPHF RE (CL) fuse 82 98566094 5,5-Restricted SCPHF RE (CL) fuse 89 99614654 5-Restricted SCPHF RE (CL) fuse 98 100597694 4-Restricted SCPHF RE (CL) fuse 103 100659134 3-Restricted SCPHF RE (CL) fuse 104 100662974 2-Restricted SCPHF RE (CL) fuse 113 114294734 5,5,5-Restricted SCPHF RE (CL) fuse 127 115343294 5,5-Restricted SCPHF RE (CL) fuse 141 116391854 5-Restricted SCPHF RE (CL) fuse 150 117374894 4-Restricted SCPHF RE (CL) fuse 156 117436334 3-Restricted SCPHF RE (CL) fuse 159 117440174 2-Restricted SCPHF RE (CL) fuse 163 117440414 SCPHF Random Extension (CLS) fuse 164 117440504 CPHF Random Extension (CLS) fuse 236 134217614 SCPHF Random Extension (CLS) fuse 268 193100429 SCPHF Random Extension (CLS) fuse fuse 269 260891369 Add 1 factors 289 268435408 Power CT17^2 290 336327148 Add 1 factors 291 367263298 Add 2 factors 292 389896048 Add 3 factors 294 418906251 Add 5 factors 295 433811236 Add 6 factors 305 443642608 Add 16 factors 306 482199664 Add 17 factors 312 518505358 Martirosyan-TVT 313 518622958 Martirosyan-TVT variant 316 518736718 Martirosyan-TVT 317 518871808 Martirosyan-TVT variant 318 519006898 Martirosyan-TVT 512 536870414 perfect hash family32,512,16,c fuse 513 536870816 perfect hash family32,513,17 514 617715356 Add 1 factors 515 664546406 Add 2 factors 536 669049222 Martirosyan-TVT 538 736840162 Martirosyan-TVT 544 744384201 Martirosyan-TVT 545 744613161 Martirosyan-TVT variant 546 745488709 Martirosyan-TVT 547 758722133 Martirosyan-TVT variant 550 774567013 Martirosyan-TVT 551 774723893 Martirosyan-TVT variant 557 774881029 Martirosyan-TVT variant 568 775527617 Martirosyan-TVT 578 776444897 Martirosyan-TVT 625 804257488 Power CT25^2 639 805305678 perfect hash family6,639,236 641 864188493 perfect hash family6,651,237S5 648 889126757 Power N-CT41^2Trin1,2,24 663 889126802 Power N-CT41^2T24T2 664 889192277 Power N-CT41^2Arc(2)T24 680 889192322 Power N-CT41^2T24T1 697 889192367 Power N-CT41^2T24 702 896487153 Power N-CT41^2T23T2 703 896552628 Power N-CT41^2Arc(2)T23 720 896552673 Power N-CT41^2T23T1 738 896552718 Power N-CT41^2T23 741 910249293 Power N-CT41^2T22T2 742 910314768 Power N-CT41^2Arc(2)T22 760 910314813 Power N-CT41^2T22T1 779 910314858 Power N-CT41^2T22 780 919395461 Power N-CT41^2T21T2 781 919460936 Power N-CT41^2Arc(2)T21 800 919460981 Power N-CT41^2T21T1 820 919461026 Power N-CT41^2T21 822 920584037 Power N-CT41^2Trin2,8,15 825 920584082 Power N-CT41^2T16T8 840 920649557 Power N-CT41^2Trin1,8,15 858 920649602 Power N-CT41^2T15T8 870 921632597 Power N-CT41^2Trin2,6,15 875 921632642 Power N-CT41^2T16T6 890 921698117 Power N-CT41^2Trin1,6,15 910 921698162 Power N-CT41^2T15T6 929 922550117 Power N-CT41^2Trin2,2,16 966 922615637 Power N-CT41^2Trin2,2,15 975 922615682 Power N-CT41^2T16T2 990 922681157 Power N-CT41^2Trin1,2,15 1014 922681202 Power N-CT41^2T15T2 1025 922681247 Power N-CT41^2T16 1040 922746722 Power N-CT41^2T15T1 1066 922746767 Power N-CT41^2T15 1089 935329682 Power N-CT41^2T8T8 1101 936312677 Power N-CT41^2Trin2,6,8 1128 936378197 Power N-CT41^2Trin1,6,8 1155 936378242 Power N-CT41^2T8T6 1225 937295717 Power N-CT41^2Trin2,2,8 1256 937361237 Power N-CT41^2Trin1,2,8 1287 937361282 Power N-CT41^2T8T2 1288 937426757 Power N-CT41^2Arc(2)T8 1320 937426802 Power N-CT41^2T8T1 1353 937426847 Power N-CT41^2T8 1365 938409842 Power N-CT41^2T6T2 1366 938475317 Power N-CT41^2Arc(2)T6 1400 938475362 Power N-CT41^2T6T1 1435 938475407 Power N-CT41^2T6 1447 939327317 Power N-CT41^2Trin2,2,2 1484 939392837 Power N-CT41^2Trin1,2,2 1521 939392882 Power N-CT41^2T2T2 1522 939458357 Power N-CT41^2Arc(2)T2 1560 939458402 Power N-CT41^2T2T1 1599 939458447 Power N-CT41^2T2 1600 939523922 Power N-CT41^2T1T1 1640 939523967 Power N-CT41^2T1 1681 939524012 Power N-CT41^2 1682 1049600552 Add 1 factors 1683 1110190802 Add 2 factors 1833 1130298902 Power N-CT47^2T8 1880 1130364422 Power N-CT47^2T7 1927 1130364467 Power N-CT47^2T6 1964 1141898582 Power N-CT53^2Trin2,2,13 2013 1141898627 Power N-CT53^2Trin2,2,12 2040 1142947142 Power N-CT53^2T13T2 2091 1142947187 Power N-CT53^2T12T2 2120 1143995702 Power N-CT53^2T13 2173 1143995747 Power N-CT53^2T12 2213 1145044502 perfect hash family14,2213,51 2258 1156468067 Power N-CT59^2Trin1,3,18 2296 1156529507 Power N-CT59^2T18T3 2503 1156578662 Power N-CT53^2Trin2,2,2 2601 1157627222 Power N-CT53^2T2T2 2703 1158675782 Power N-CT53^2T2 2812 1159724342 Power N-CT53^2+3 2856 1171209542 Power N-CT59^2T8T3 2977 1171213622 Power N-CT59^2Trin3,3,3 3083 1172196662 Power N-CT59^2Trin1,3,3 3111 1172254022 Power N-CT61^2T10 3136 1172258102 Power N-CT59^2T3T3 3139 1173118262 Power N-CT59^2Arc(3)T3 3193 1173179702 Power N-CT59^2Arc(2)T3 3248 1173241142 Power N-CT59^2T3T1 3416 1173302582 Power N-CT61^2T5 3538 1174285622 Power N-CT61^2T3 3723 1174347062 Power N-CT61^2+2 3724 1174400822 Power N-CT61^2+3 3726 1174404182 perfect hash family14,3726,66 3751 1201667222 Power N-CT67^2Arc(12) 3807 1215298742 Power N-CT67^2Arc(11) 3825 1226833129 Power N-CT73^2Trin7,7,9 3943 1226833369 Power N-CT73^2Trin7,7,7 3969 1240456729 Power N-CT73^2T10T10 4032 1240460569 Power N-CT73^2T10T9 4158 1240460809 Power N-CT73^2T10T7 4224 1240464649 Power N-CT73^2T9T7 4356 1240464889 Power N-CT73^2T7T7 4599 1254092329 Power N-CT73^2T10 4672 1254096169 Power N-CT73^2T9 4818 1254096409 Power N-CT73^2T7 4977 1266675049 Power N-CT79^2T16 5056 1266678889 Power N-CT79^2T15 5214 1266679129 Power N-CT79^2T13 5329 1267727929 Power N-CT73^2 5347 1277164729 Power N-CT83^2Arc(2)T17 5412 1278213289 Power N-CT83^2T17T1 5607 1279257769 Power N-CT89^2T26 5696 1279261609 Power N-CT89^2T25 5874 1279261849 Power N-CT89^2T23 6244 1281359209 Power N-CT79^2+3 6253 1286602009 Power N-CT83^2Arc(8) 6329 1287650569 Power N-CT83^2Arc(7) 6406 1288699129 Power N-CT83^2Arc(6) 6484 1289747689 Power N-CT83^2Arc(5) 6563 1290796249 Power N-CT83^2Arc(4) 6592 1291795369 perfect hash family13,10609,103T39 6798 1291795609 perfect hash family13,10609,103T37 7298 1293941929 Power N-CT89^2T7 7921 1294990489 Power N-CT89^2 7954 1305738409 Power N-CT97^2T15 8036 1306414249 Power N-CT101^2T19T3 8446 1306475689 perfect hash family13,10609,103T21 8633 1306786969 Power N-CT97^2T8 8722 1307462809 Power N-CT101^2T12T3 9167 1307524249 perfect hash family13,10609,103T14 9410 1307770009 Power N-CT97^2+1 9604 1308445849 Power N-CT101^2T3T3 10000 1308507289 perfect hash family13,10609,103T5

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