Table for CAN(6,k,20) for k up to 10000

Last Updated Fri Mar 27 17:29:25 MST 2015

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,20) 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 64000000 composition 8 70901841 Augment OA 9 74615592 Augment OA 10 78509088 Augment OA 11 82584720 Augment OA 12 86844605 Augment OA 13 91286154 Augment OA 14 95902380 Augment OA 15 100688940 Augment OA 16 105640344 Augment OA 17 110740896 Augment OA 18 115969812 Augment OA 19 121310952 Augment OA 20 126740694 Augment OA 24 148035883 orthogonal array fuse fuse fuse 26 244140615 orthogonal array fuse fuse fuse fuse fuse 28 387420475 orthogonal array fuse fuse fuse fuse fuse fuse fuse 29 517973590 Martirosyan-TVT variant 30 523106174 Martirosyan-TVT 31 535219514 Martirosyan-TVT variant 32 540857182 Martirosyan-TVT 33 554789557 Martirosyan-TVT variant 34 561165960 Martirosyan-TVT 35 573095578 Martirosyan-TVT variant 36 576322594 Martirosyan-TVT 37 588026791 Martirosyan-TVT variant 38 590461066 Martirosyan-TVT 39 601857688 Martirosyan-TVT variant 40 609558548 Martirosyan-TVT 41 655815861 Martirosyan-TVT variant 42 697278394 Martirosyan-TVT 43 697398294 Martirosyan-TVT variant 44 698077962 Martirosyan-TVT 45 698221962 Martirosyan-TVT variant 46 698925774 Martirosyan-TVT 47 699093942 Martirosyan-TVT variant 48 700941310 Martirosyan-TVT 49 955057570 Add 1 factors 50 1060979477 Martirosyan-TVT 51 1061134639 Martirosyan-TVT variant 52 1065196001 Martirosyan-TVT 53 1334420461 perfect hash family11,53,19 55 1383288139 perfect hash family11,60,20S2 57 1388717881 perfect hash family11,60,20T1 60 1394147623 perfect hash family11,60,20 65 1460578448 perfect hash family16,65,13 66 1534438064 perfect hash family16,66,14 67 1569750933 perfect hash family15,80,16S3 71 1574702337 perfect hash family15,80,16S2 75 1579653741 perfect hash family15,80,16T1 80 1584605145 Power CT16^2Tlev 82 1592918804 Power CT16^2T5S15 96 1596266793 Power CT16^2TD(4):4,4,4,4,4 112 1602603812 Power CT16^2Arc(18):9 twos,0 ones 120 1611023024 Power CT16^2Arc(16) 121 1615974428 Power CT16^2Arc(15) 123 1620925832 Power CT16^2Arc(14) 126 1625877236 Power CT16^2Arc(13) 130 1630828640 Power CT16^2Arc(12) 135 1635780044 Power CT16^2Arc(11) 141 1640731448 Power CT16^2Arc(10) 148 1645682852 Power CT16^2Arc(9) 156 1650634256 Power CT16^2Arc(8) 165 1655585660 Power CT16^2Arc(7) 175 1660537064 Power CT16^2Arc(6) 186 1665488468 Power CT16^2Arc(5) 198 1670439872 Power CT16^2Arc(4) 211 1675391276 Power CT16^2Arc(3) 225 1680342680 Power CT16^2T1T1 240 1685294084 Power CT16^2T1 256 1690245488 Power CT16^2 272 1766753768 Power CT17^2T1 289 1771854320 Power CT17^2 290 1855516976 Power CT17^2+1 291 1919610656 Power CT19^2Arc(4) 307 1924951796 Power CT19^2Arc(3) 324 1930292936 Power CT19^2T1T1 342 1935634076 Power CT19^2T1 361 1940975216 Power CT19^2 362 2027851088 Power CT19^2+1 380 2320553992 Power CT23^2T4T3 400 2325983734 Power CT23^2T3T3 414 2336508041 Power CT23^2T5 437 2341849181 Power CT23^2T4 460 2347278923 Power CT23^2T3 529 2368573873 perfect hash family16,529,23,c fuse fuse fuse 530 2368574112 Power CT23^2+1 531 2882920452 Add 1 factors 532 3067805652 Add 2 factors 533 3211597652 Add 3 factors 534 3369054408 Add 5 factors 535 3369054647 Add 5 factors 536 3450817350 Add 6 factors 553 3617935628 Power CT25^2Arc(3) 576 3714040360 Power CT25^2T1T1 600 3810145092 Power CT25^2T1 625 3906249615 perfect hash family16,625,25,c fuse fuse fuse fuse fuse 626 3906249824 Power CT25^2+1 627 4599285464 Add 1 factors 628 4836701864 Add 2 factors 629 4982165864 Add 3 factors 630 5070743782 Add 5 factors 631 5142649763 Add 5 factors 632 5246451188 Add 6 factors 648 5617720739 Add 23 factors 649 5713534578 Add 23 factors 651 5768888004 Power CT27^2Arc(3) 672 5896682063 Martirosyan-TVT 673 5907564666 Martirosyan-TVT variant 676 5912167864 Power CT27^2T1T1 684 5933704717 Martirosyan-TVT 720 5942974639 Martirosyan-TVT 721 5952285950 Martirosyan-TVT variant 722 5961597261 Martirosyan-TVT 724 6086640333 Martirosyan-TVT 730 6198727584 Power CT27^2+1 736 6404347218 Martirosyan-TVT 760 6408409988 Martirosyan-TVT 761 6413839730 Martirosyan-TVT variant 768 6431786064 Martirosyan-TVT 769 6443261964 Martirosyan-TVT variant 771 6459916392 Martirosyan-TVT variant 782 6462505656 Martirosyan-TVT 783 6470317227 Martirosyan-TVT variant 800 6474119760 Martirosyan-TVT 816 6484644067 Martirosyan-TVT 817 6486080740 Martirosyan-TVT variant 828 6490118281 Martirosyan-TVT 829 6503194947 Martirosyan-TVT variant 864 6507001691 Martirosyan-TVT 865 6507927387 Martirosyan-TVT variant 874 6508853083 Martirosyan-TVT 875 6521906289 Martirosyan-TVT variant 912 6525713033 Martirosyan-TVT 913 6536335937 Martirosyan-TVT variant 920 6602467343 Martirosyan-TVT 921 6632193167 Martirosyan-TVT variant 951 6636088342 Martirosyan-TVT variant 960 6654650130 Martirosyan-TVT 961 6680465598 Martirosyan-TVT variant 966 6736058968 Martirosyan-TVT 967 6736059911 Martirosyan-TVT variant 969 6736060854 Martirosyan-TVT variant 979 6738767938 Martirosyan-TVT variant 1009 6741475022 Martirosyan-TVT variant 1012 6744182106 Martirosyan-TVT 1013 6744183052 Martirosyan-TVT variant 1058 6744183998 Martirosyan-TVT 1059 6775273581 Martirosyan-TVT variant 1060 6806362925 Martirosyan-TVT 1062 7496350205 Martirosyan-TVT 1064 7817837805 Martirosyan-TVT 1066 8019389805 Martirosyan-TVT 1068 8244658625 Martirosyan-TVT 1070 8250599841 Martirosyan-TVT 1076 8500583704 Power N-CT41^2T5S13 1105 8512287901 Power N-CT41^2T4S13 1134 8514722176 Power N-CT41^2T3S13 1164 8526118798 Power N-CT41^2T2S13 1198 8533819658 Power N-CT41^2Arc(14) 1226 8580076971 Power N-CT41^2Arc(13) 1255 8626334284 Power N-CT41^2Arc(12) 1285 8672591597 Power N-CT41^2Arc(11) 1316 8718848910 Power N-CT41^2Arc(10) 1348 8765106223 Power N-CT41^2Arc(9) 1381 8811363536 Power N-CT41^2Arc(8) 1415 8857620849 Power N-CT41^2Arc(7) 1450 8903878162 Power N-CT41^2Arc(6) 1486 8950135475 Power N-CT41^2Arc(5) 1523 8996392788 Power N-CT41^2Arc(4) 1561 9042650101 Power N-CT41^2Arc(3) 1600 9088907414 Power N-CT41^2T1T1 1640 9135164727 Power N-CT41^2T1 1681 9181422040 Power N-CT41^2 1692 9664543826 Power N-CT47^2T11 1720 9675736356 Power N-CT43^2T3 1739 9676248023 Power N-CT47^2T10 1748 9678514130 Power N-CT47^2T9T1 1786 9678682298 Power N-CT47^2T9 1794 9689910752 Power N-CT47^2T8T1 1833 9690078920 Power N-CT47^2T8 1840 9697611612 Power N-CT47^2T7T1 1880 9697779780 Power N-CT47^2T7 1886 9743868925 Power N-CT47^2T6T1 1927 9744037093 Power N-CT47^2T6 1939 9784699234 Power N-CT47^2Trin2,2,2 1982 9785403046 Power N-CT47^2Trin1,2,2 2025 9785571214 Power N-CT47^2T2T2 2026 9786106858 Power N-CT47^2Arc(2)T2 2070 9786275026 Power N-CT47^2T2T1 2115 9786443194 Power N-CT47^2T2 2116 9786978838 Power N-CT47^2T1T1 2162 9787147006 Power N-CT47^2T1 2209 9787315174 Power N-CT47^2 2210 9813178326 Power N-CT47^2+1 2211 10775980526 Add 1 factors 2212 11131812526 Add 2 factors 2213 11325308526 Add 3 factors 2214 11473874188 Add 5 factors 2215 11499737340 Add 5 factors 2216 11644122283 Add 6 factors 2232 12219732062 Add 23 factors 2233 12245595214 Add 23 factors 2234 12909079174 Add 25 factors 2235 12934942326 Add 25 factors 2236 13757725414 Add 23 factors 2237 13906291076 Add 23 factors 2238 13932154228 Add 23 factors 2239 14076539171 Add 23 factors 2257 14518572324 Power CT49^2Arc(3) 2304 14772688584 Power CT49^2T1T1 2352 15026804844 Power CT49^2T1 2366 15264621049 Power CT31^3T18T18T17 2548 15269237275 Power CT31^3T18T17T17 2744 15273853501 Power CT31^3T17T17T17 2940 15278640061 Power CT31^3T17T17T16 3150 15283426621 Power CT31^3T17T16T16 3375 15288213181 Power CT31^3T16T16T16 3600 15293164585 Power CT31^3T16T16T15 3840 15298115989 Power CT31^3T16T15T15 4096 15303067393 Power CT31^3T15T15T15 4352 15308167945 Power CT31^3T15T15T14 4624 15313268497 Power CT31^3T15T14T14 4913 15318369049 Power CT31^3T14T14T14 5202 15323597965 Power CT31^3T14T14T13 5508 15328826881 Power CT31^3T14T13T13 5832 15334055797 Power CT31^3T13T13T13 6156 15339396937 Power CT31^3T13T13T12 6498 15344738077 Power CT31^3T13T12T12 6859 15350079217 Power CT31^3T12T12T12 7220 15355508959 Power CT31^3T12T12T11 7344 15360892952 Power CT31^3T14T13T7 7600 15360938701 Power CT31^3T12T11T11 7776 15366121868 Power CT31^3T13T13T7 8000 15366368443 Power CT31^3T11T11T11 8208 15371463008 Power CT31^3T13T12T7 8664 15376804148 Power CT31^3T12T12T7 9120 15382233890 Power CT31^3T12T11T7 9600 15387663632 Power CT31^3T11T11T7 9792 15392959023 Power CT31^3T14T7T7 10000 15398187939 Power CT31^3T13T7T7

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