Table for CAN(6,k,8) for k up to 10000

Last Updated Fri Sep 20 11:45:18 MST 2013

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,8) 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 9 262144 orthogonal array 10 487424 extended OA (Colbourn) 11 716800 Add 1 factors 12 946176 Add 2 factors 13 1175552 Add 3 factors 16 1179648 double OA (Colbourn-Zhou) 18 1211904 double OA (Colbourn-Zhou) 19 1670208 Add 1 factors 20 2060767 Martirosyan-Tran van Trung 21 2473024 Add 3 factors 22 2702400 Add 4 factors 24 2870848 Add 8 factors 25 2924608 Add 8 factors 26 2931776 Add 8 factors 27 3390080 Add 8 factors 28 3816479 Add 8 factors 29 4232320 Add 8 factors 30 4561408 Martirosyan-Tran van Trung 32 4659616 Martirosyan-Tran van Trung 36 4724608 Martirosyan-Tran van Trung 37 5411840 Add 1 factors 38 5678623 Martirosyan-Tran van Trung 40 6085550 Martirosyan-Tran van Trung 44 6755840 Add 8 factors 45 7443072 Add 8 factors 46 8079903 Add 8 factors 48 8486830 Add 8 factors 50 8741312 Martirosyan-Tran van Trung 52 8754752 Martirosyan-Tran van Trung 54 9573551 Martirosyan-Tran van Trung 56 10031310 Martirosyan-Tran van Trung 58 10765400 Martirosyan-Tran van Trung 60 11094488 Martirosyan-Tran van Trung 64 11297880 Martirosyan-Tran van Trung 72 11389752 Martirosyan-Tran van Trung 73 12497208 Add 1 factors 74 12955512 Add 2 factors 75 13385592 Add 3 factors 76 13614968 Add 4 factors 80 13844344 Add 8 factors 81 14951800 Add 8 factors 82 15502280 Add 8 factors 83 16125896 Add 8 factors 84 16151040 Martirosyan-Tran van Trung 88 16197177 Martirosyan-Tran van Trung 90 16920074 Martirosyan-Tran van Trung 91 17485808 Power CT16^2TD(8):5,5,5 100 17489904 Power CT16^2T6T6 110 17719280 Power CT16^2T6T5 121 17948656 Power CT16^2T5T5 144 17956848 Power CT16^2T7 160 18182128 Power CT16^2T6 176 18411504 Power CT16^2T5 192 18640880 Power CT16^2T4 208 18870256 Power CT16^2T3 256 18874352 Power CT16^2 272 19358192 Power CT17^2T1 290 19390448 Power CT17^2+1 291 21445032 Add 1 factors 292 22477224 Add 2 factors 293 23108008 Add 3 factors 294 23337384 Add 4 factors 297 23400496 Add 8 factors 298 23566760 Add 8 factors 307 25348400 Power CT19^2Arc(3) 324 25806704 Power CT19^2T1T1 342 26265008 Power CT19^2T1 361 26723312 Power CT19^2 362 28984424 Add 1 factors 363 30019752 Add 2 factors 364 30650536 Add 3 factors 365 30879912 Add 4 factors 369 31109288 Add 8 factors 370 33046712 Add 9 factors 371 34405728 Add 8 factors 372 35036512 Add 8 factors 373 35265888 Add 8 factors 377 35495264 Add 8 factors 378 37432688 Add 9 factors 384 37515232 perfect hash family32,512,16T4 416 37744608 perfect hash family32,512,16T3 512 37748704 perfect hash family32,512,16 514 38780896 perfect hash family32,514,18 515 41145832 Add 1 factors 516 41905304 Add 4 factors 520 42134680 Add 8 factors 521 43166872 Add 8 factors 522 43270696 Add 8 factors 523 45237784 Add 9 factors 530 45933552 Power CT23^2+1 540 45990771 Martirosyan-Tran van Trung 544 46058211 Martirosyan-Tran van Trung 564 46090467 Martirosyan-Tran van Trung 576 46345379 Martirosyan-Tran van Trung 600 46739952 Power CT25^2T1 625 46793712 Power CT25^2 626 46908400 Power CT25^2+1 627 49469336 Add 1 factors 628 50589784 Add 2 factors 629 51220568 Add 3 factors 630 51449944 Add 4 factors 633 51564632 Add 8 factors 634 51679320 Add 8 factors 651 52866352 Power CT27^2Arc(3) 676 53324656 Power CT27^2T1T1 702 53782960 Power CT27^2T1 729 54241264 Power CT27^2 730 57101912 Add 1 factors 731 58241176 Add 2 factors 732 58900632 Add 3 factors 733 59130008 Add 4 factors 737 59359384 Add 8 factors 738 61532488 Add 9 factors 754 62184241 Power N-CT29^2T3 756 62226704 Power N-CT29^2T2T1 757 62237262 Power N-CT29^2Arc(3) 783 62642545 Power N-CT29^2T2 784 62653103 Power N-CT29^2T1T1 812 63068944 Power N-CT29^2T1 841 63484785 Power N-CT29^2 842 66727745 Add 1 factors 843 68062785 Add 2 factors 844 68743745 Add 3 factors 845 68973121 Add 4 factors 868 69051088 Power N-CT31^2T3 870 69368721 Power N-CT31^2T2T1 899 69466929 Power N-CT31^2T2 900 69697809 Power N-CT31^2T1T1 930 69796017 Power N-CT31^2T1 962 69894225 Power N-CT31^2+1 964 70869105 Power N-CT31^2+3 966 72243569 Power N-CT37^2Arc(13) 1024 72401493 Martirosyan-Tran van Trung 1028 74086293 Martirosyan-Tran van Trung 1044 74305265 Power N-CT37^2Arc(10) 1072 74992497 Power N-CT37^2Arc(9) 1101 75679729 Power N-CT37^2Arc(8) 1131 76366961 Power N-CT37^2Arc(7) 1162 77054193 Power N-CT37^2Arc(6) 1194 77741425 Power N-CT37^2Arc(5) 1227 78428657 Power N-CT37^2Arc(4) 1261 79115889 Power N-CT37^2Arc(3) 1296 79803121 Power N-CT37^2T1T1 1332 80490353 Power N-CT37^2T1 1369 81177585 Power N-CT37^2 1370 84815849 Add 1 factors 1371 86229289 Add 2 factors 1372 87003433 Add 3 factors 1373 87232809 Add 4 factors 1377 87462185 Add 8 factors 1381 89219426 Power N-CT41^2Arc(8) 1415 89889716 Power N-CT41^2Arc(7) 1450 90560006 Power N-CT41^2Arc(6) 1486 91230296 Power N-CT41^2Arc(5) 1523 91900586 Power N-CT41^2Arc(4) 1548 92550514 Power N-CT43^2T7 1561 92570876 Power N-CT41^2Arc(3) 1591 93237746 Power N-CT43^2T6 1600 93241166 Power N-CT41^2T1T1 1634 93504529 Power N-CT43^2T5 1720 93911456 Power N-CT43^2T3 1850 94581746 Power N-CT43^2+1 1851 98433202 Add 1 factors 1852 100007026 Add 2 factors 1853 100813426 Add 3 factors 1854 101042802 Add 4 factors 1858 101272178 Add 8 factors 1859 104014538 Add 9 factors 1860 106697458 Add 8 factors 1861 107503858 Add 8 factors 1862 107733234 Add 8 factors 1866 107962610 Add 8 factors 1867 110704970 Add 9 factors 1868 113387890 Add 8 factors 1869 114194290 Add 8 factors 1870 114423666 Add 8 factors 1874 114653042 Add 8 factors 1895 114946699 Power N-CT47^2Trin1,3,3 1896 114997100 Power N-CT47^2Trin2,2,3 1936 115353626 Power N-CT47^2T3T3 1938 115633931 Power N-CT47^2Trin1,2,3 1939 115684332 Power N-CT47^2Trin2,2,2 1980 116040858 Power N-CT47^2T3T2 1981 116270762 Power N-CT47^2Arc(2)T3 1982 116321163 Power N-CT47^2Trin1,2,2 1983 116551067 Power N-CT47^2Arc(3)T2 2024 116677689 Power N-CT47^2T3T1 2025 116728090 Power N-CT47^2T2T2 2026 116957994 Power N-CT47^2Arc(2)T2 2068 117084616 Power N-CT47^2T3 2070 117364921 Power N-CT47^2T2T1 2071 117594825 Power N-CT47^2Arc(3) 2115 117771848 Power N-CT47^2T2 2116 118001752 Power N-CT47^2T1T1 2162 118408679 Power N-CT47^2T1 2210 118815606 Power N-CT47^2+1 2212 122378354 Power N-CT47^2+3 2239 124204112 Power N-CT53^2Arc(12) 2281 125022911 Power N-CT53^2Arc(11) 2324 125841710 Power N-CT53^2Arc(10) 2368 126660509 Power N-CT53^2Arc(9) 2413 127479308 Power N-CT53^2Arc(8) 2459 128298107 Power N-CT53^2Arc(7) 2506 129116906 Power N-CT53^2Arc(6) 2554 129935705 Power N-CT53^2Arc(5) 2603 130754504 Power N-CT53^2Arc(4) 2653 131573303 Power N-CT53^2Arc(3) 2704 132392102 Power N-CT53^2T1T1 2916 133155169 Power CT31^3T22T13T13 3240 133380449 Power CT31^3T21T13T13 3564 133609825 Power CT31^3T20T13T13 3888 133839201 Power CT31^3T19T13T13 4096 134008161 Power CT31^3T15T15T15 4608 134040417 Power CT31^3T15T15T13 5184 134072673 Power CT31^3T15T13T13 5832 134104929 Power CT31^3T13T13T13 6156 134563233 Power CT31^3T13T13T12 6480 134953792 Power CT31^3T13T13T11 6498 135021537 Power CT31^3T13T12T12 6804 135366049 Power CT31^3T13T13T10 6840 135412096 Power CT31^3T13T12T11 6859 135479841 Power CT31^3T12T12T12 7128 135595425 Power CT31^3T13T13T9 7776 135763873 Power CT31^3T13T13T7 8100 135817633 Power CT31^3T13T13T6 8424 135824801 Power CT31^3T13T13T5 8550 136275937 Power CT31^3T13T12T6 8892 136283105 Power CT31^3T13T12T5 9000 136666496 Power CT31^3T13T11T6 9360 136673664 Power CT31^3T13T11T5 9386 136741409 Power CT31^3T12T12T5 9450 137078753 Power CT31^3T13T10T6 9828 137085921 Power CT31^3T13T10T5 9880 137131968 Power CT31^3T12T11T5 9900 137308129 Power CT31^3T13T9T6 10000 137315297 Power CT31^3T13T9T5

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