Table for CAN(6,k,8) 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,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 450372 orthogonal array fuse postop NCK 11 679748 Add 1 factors 12 909124 Add 2 factors 13 1138500 Add 3 factors 16 1179648 double OA (Colbourn-Zhou) 18 1211904 double OA (Colbourn-Zhou) 19 1670208 Add 1 factors 20 2019283 Martirosyan-TVT 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 3774995 Add 8 factors 29 4232320 Add 8 factors 30 4499248 Martirosyan-TVT 31 4501285 Martirosyan-TVT variant 32 4599493 Martirosyan-TVT 33 4634444 Martirosyan-TVT variant 34 4667180 Martirosyan-TVT 36 4716880 Martirosyan-TVT 37 5404112 Add 1 factors 38 5584844 Martirosyan-TVT 39 6022560 Martirosyan-TVT variant 40 6038928 Martirosyan-TVT 41 6665676 Add 8 factors 42 6698412 Add 8 factors 44 6748112 Add 8 factors 45 7435344 Add 8 factors 46 7846180 Add 8 factors 47 8283896 Add 8 factors 48 8300264 Add 8 factors 49 8659340 Martirosyan-TVT variant 50 8683884 Martirosyan-TVT 52 8747024 Martirosyan-TVT 53 9283105 Martirosyan-TVT variant 54 9307649 Martirosyan-TVT 56 9694132 Martirosyan-TVT 57 10151457 Martirosyan-TVT variant 58 10249633 Martirosyan-TVT 60 10516561 Martirosyan-TVT 61 10518598 Martirosyan-TVT variant 62 10543142 Martirosyan-TVT 64 10641350 Martirosyan-TVT 66 10676301 Martirosyan-TVT 68 10709037 Martirosyan-TVT 72 10758737 Martirosyan-TVT 73 11866193 Add 1 factors 74 12324497 Add 2 factors 75 12754577 Add 3 factors 76 12773875 Martirosyan-TVT 78 13211591 Martirosyan-TVT 80 13213329 Add 8 factors 81 13863877 Martirosyan-TVT variant 82 13871038 Martirosyan-TVT 84 13903774 Martirosyan-TVT 88 13953474 Martirosyan-TVT 90 14640706 Martirosyan-TVT 92 15091820 Martirosyan-TVT 94 15529536 Martirosyan-TVT 96 15545904 Martirosyan-TVT 97 16206918 Martirosyan-TVT variant 98 16506798 Martirosyan-TVT 100 16531342 Martirosyan-TVT 104 16594482 Martirosyan-TVT 106 17130563 Martirosyan-TVT 108 17155107 Martirosyan-TVT 112 17557025 Martirosyan-TVT 121 17874552 Power CT16^2T5T5 144 17956848 Power CT16^2T7 160 18145076 Power CT16^2T6 176 18374452 Power CT16^2T5 192 18603828 Power CT16^2T4 208 18833204 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 28844480 Add 1 factors 363 29879808 Add 2 factors 364 30510592 Add 3 factors 365 30739968 Add 4 factors 369 30969344 Add 8 factors 370 32866784 Add 9 factors 371 34125840 Add 8 factors 372 34756624 Add 8 factors 373 34986000 Add 8 factors 377 35215376 Add 8 factors 378 37112816 Add 9 factors 384 37478180 perfect hash family32,512,16T4 416 37707556 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 541 45074625 Martirosyan-TVT variant 544 45142065 Martirosyan-TVT 564 45246561 Martirosyan-TVT 565 45372449 Martirosyan-TVT variant 576 45501473 Martirosyan-TVT 577 46024017 Martirosyan-TVT variant 578 46546561 Martirosyan-TVT 600 46739952 Power CT25^2T1 625 46793712 Power CT25^2 626 46908400 Power CT25^2+1 627 49469336 Add 1 factors 628 50588888 Add 2 factors 629 51219672 Add 3 factors 630 51449048 Add 4 factors 633 51563736 Add 8 factors 634 51678424 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 57101744 Add 1 factors 731 58240112 Add 2 factors 732 58899568 Add 3 factors 733 59128944 Add 4 factors 737 59358320 Add 8 factors 738 61530976 Add 9 factors 757 62112810 Power N-CT29^2Arc(3) 784 62570135 Power N-CT29^2T1T1 812 63027460 Power N-CT29^2T1 841 63484785 Power N-CT29^2 842 66727409 Add 1 factors 868 66792970 Power N-CT31^2T3 870 67248258 Power N-CT31^2T2T1 899 67250295 Power N-CT31^2T2 900 67515186 Power N-CT31^2T1T1 930 67517223 Power N-CT31^2T1 961 67519260 Power N-CT31^2 962 68992380 Power N-CT31^2+1 963 69516645 Power N-CT31^2+2 964 70007685 Power N-CT31^2+3 1020 71441499 Martirosyan-TVT 1024 71454981 Martirosyan-TVT 1025 72843843 Martirosyan-TVT variant 1028 73170147 Martirosyan-TVT 1044 74189345 Power N-CT37^2Arc(10) 1072 74876577 Power N-CT37^2Arc(9) 1101 75563809 Power N-CT37^2Arc(8) 1131 76251041 Power N-CT37^2Arc(7) 1162 76938273 Power N-CT37^2Arc(6) 1194 77625505 Power N-CT37^2Arc(5) 1227 78312737 Power N-CT37^2Arc(4) 1261 78999969 Power N-CT37^2Arc(3) 1296 79687201 Power N-CT37^2T1T1 1332 80374433 Power N-CT37^2T1 1369 81061665 Power N-CT37^2 1370 83772645 Power N-CT37^2+1 1371 86113369 Add 2 factors 1372 86887513 Add 3 factors 1373 87116889 Add 4 factors 1377 87346265 Add 8 factors 1381 88305466 Power N-CT41^2Arc(8) 1415 88932214 Power N-CT41^2Arc(7) 1450 89558962 Power N-CT41^2Arc(6) 1486 90185710 Power N-CT41^2Arc(5) 1523 90812458 Power N-CT41^2Arc(4) 1561 91439206 Power N-CT41^2Arc(3) 1600 92065954 Power N-CT41^2T1T1 1640 92692702 Power N-CT41^2T1 1681 93319450 Power N-CT41^2 1720 93764370 Power N-CT43^2T3 1723 94324454 Power N-CT43^2Arc(3) 1764 94374154 Power N-CT43^2T1T1 1806 94423854 Power N-CT43^2T1 1850 94473554 Power N-CT43^2+1 1851 98325010 Add 1 factors 1852 99897938 Add 2 factors 1853 100704338 Add 3 factors 1854 100933714 Add 4 factors 1858 101163090 Add 8 factors 1859 103905050 Add 9 factors 1860 106587474 Add 8 factors 1861 107393874 Add 8 factors 1862 107623250 Add 8 factors 1866 107852626 Add 8 factors 1867 110594586 Add 9 factors 1895 112465246 Power N-CT47^2Trin1,3,3 1898 112687882 Power N-CT47^2Arc(4)T3 1936 112902962 Power N-CT47^2T3T3 1939 113125598 Power N-CT47^2Arc(3)T3 1942 113348234 Power N-CT47^2Arc(6) 1981 113563314 Power N-CT47^2Arc(2)T3 1984 113785950 Power N-CT47^2Arc(5) 2024 114001030 Power N-CT47^2T3T1 2027 114223666 Power N-CT47^2Arc(4) 2068 114438746 Power N-CT47^2T3 2071 114661382 Power N-CT47^2Arc(3) 2116 115099098 Power N-CT47^2T1T1 2162 115536814 Power N-CT47^2T1 2209 115974530 Power N-CT47^2 2210 116203682 Power N-CT47^2+1 2211 120128610 Add 1 factors 2212 121574362 Power N-CT47^2+3 2213 122557218 Add 3 factors 2214 122786594 Add 4 factors 2217 122786818 Add 8 factors 2218 123015970 Add 8 factors 2239 123530484 Power N-CT53^2Arc(12) 2281 124066565 Power N-CT53^2Arc(11) 2324 124602646 Power N-CT53^2Arc(10) 2368 125138727 Power N-CT53^2Arc(9) 2413 125674808 Power N-CT53^2Arc(8) 2459 126210889 Power N-CT53^2Arc(7) 2506 126746970 Power N-CT53^2Arc(6) 2554 127283051 Power N-CT53^2Arc(5) 2603 127819132 Power N-CT53^2Arc(4) 2653 128355213 Power N-CT53^2Arc(3) 2916 128721901 Power CT31^3T22T13T13 3240 128910129 Power CT31^3T21T13T13 3564 129139505 Power CT31^3T20T13T13 3888 129368881 Power CT31^3T19T13T13 4096 129574893 Power CT31^3T15T15T15 4212 129598257 Power CT31^3T18T13T13 4608 129607149 Power CT31^3T15T15T13 5184 129639405 Power CT31^3T15T13T13 5832 129671661 Power CT31^3T13T13T13 6156 130129965 Power CT31^3T13T13T12 6480 130479040 Power CT31^3T13T13T11 6498 130588269 Power CT31^3T13T12T12 6804 130932781 Power CT31^3T13T13T10 6840 130937344 Power CT31^3T13T12T11 6859 131046573 Power CT31^3T12T12T12 7128 131162157 Power CT31^3T13T13T9 7200 131286419 Power CT31^3T13T11T11 7776 131330605 Power CT31^3T13T13T7 8100 131384365 Power CT31^3T13T13T6 8424 131391533 Power CT31^3T13T13T5 8550 131842669 Power CT31^3T13T12T6 8892 131849837 Power CT31^3T13T12T5 9000 132191744 Power CT31^3T13T11T6 9360 132198912 Power CT31^3T13T11T5 9386 132308141 Power CT31^3T12T12T5 9450 132645485 Power CT31^3T13T10T6 9500 132650048 Power CT31^3T12T11T6 9828 132652653 Power CT31^3T13T10T5 9880 132657216 Power CT31^3T12T11T5 9900 132874861 Power CT31^3T13T9T6 10000 132882029 Power CT31^3T13T9T5

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