Table for CAN(6,k,8) 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,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).

Change t: - Change v: - + or go to Global Menu.

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 4499927 Martirosyan-TVT 31 4503581 Martirosyan-TVT variant 32 4601789 Martirosyan-TVT 33 4634444 Martirosyan-TVT variant 34 4667180 Martirosyan-TVT 36 4716880 Martirosyan-TVT 37 5404112 Add 1 factors 38 5584956 Martirosyan-TVT 39 6022581 Martirosyan-TVT variant 40 6038949 Martirosyan-TVT 41 6665676 Add 8 factors 42 6698412 Add 8 factors 44 6748112 Add 8 factors 45 7435344 Add 8 factors 46 7986236 Add 8 factors 47 8423861 Add 8 factors 48 8440229 Add 8 factors 49 8659340 Martirosyan-TVT variant 50 8683884 Martirosyan-TVT 52 8747024 Martirosyan-TVT 53 9284673 Martirosyan-TVT variant 54 9309217 Martirosyan-TVT 56 9694132 Martirosyan-TVT 57 10151457 Martirosyan-TVT variant 58 10249633 Martirosyan-TVT 60 10517240 Martirosyan-TVT 61 10520894 Martirosyan-TVT variant 62 10545438 Martirosyan-TVT 64 10643646 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 12983953 Add 4 factors 80 13213329 Add 8 factors 81 14320785 Add 8 factors 82 14537095 Martirosyan-TVT 84 14569831 Martirosyan-TVT 88 14619531 Martirosyan-TVT 90 15306763 Martirosyan-TVT 92 15857655 Martirosyan-TVT 94 16295280 Martirosyan-TVT 96 16311648 Martirosyan-TVT 98 16530759 Martirosyan-TVT 100 16555303 Martirosyan-TVT 104 16618443 Martirosyan-TVT 106 17156092 Martirosyan-TVT 108 17180636 Martirosyan-TVT 112 17565551 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 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 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 523 45237784 Add 9 factors 541 45358664 Martirosyan-TVT variant 544 45426104 Martirosyan-TVT 564 45458759 Martirosyan-TVT 565 45584647 Martirosyan-TVT variant 576 45713671 Martirosyan-TVT 577 46236215 Martirosyan-TVT variant 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 57101744 Add 1 factors 731 58241008 Add 2 factors 732 58900464 Add 3 factors 733 59129840 Add 4 factors 737 59359216 Add 8 factors 738 61532272 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 66825114 Power N-CT31^2T3 870 67278785 Power N-CT31^2T2T1 899 67282439 Power N-CT31^2T2 900 67546392 Power N-CT31^2T1T1 930 67550046 Power N-CT31^2T1 961 67553700 Power N-CT31^2 962 69026820 Power N-CT31^2+1 963 69516645 Power N-CT31^2+2 964 70007685 Power N-CT31^2+3 1024 71765396 Martirosyan-TVT 1025 73127882 Martirosyan-TVT variant 1028 73454186 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 83774325 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 88305634 Power N-CT41^2Arc(8) 1415 88932361 Power N-CT41^2Arc(7) 1450 89559088 Power N-CT41^2Arc(6) 1486 90185815 Power N-CT41^2Arc(5) 1523 90812542 Power N-CT41^2Arc(4) 1561 91439269 Power N-CT41^2Arc(3) 1600 92065996 Power N-CT41^2T1T1 1640 92692723 Power N-CT41^2T1 1681 93319450 Power N-CT41^2 1720 93764391 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 99898834 Add 2 factors 1853 100705234 Add 3 factors 1854 100934610 Add 4 factors 1858 101163986 Add 8 factors 1859 103906346 Add 9 factors 1860 106589266 Add 8 factors 1861 107395666 Add 8 factors 1862 107625042 Add 8 factors 1866 107854418 Add 8 factors 1867 110596778 Add 9 factors 1868 113279698 Add 8 factors 1869 114086098 Add 8 factors 1895 114144917 Power N-CT47^2Trin1,3,3 1896 114281257 Power N-CT47^2Trin2,2,3 1898 114507791 Power N-CT47^2Arc(4)T3 1936 114582542 Power N-CT47^2T3T3 1938 114832149 Power N-CT47^2Trin1,2,3 1939 114945416 Power N-CT47^2Arc(3)T3 1941 115195023 Power N-CT47^2Arc(4)T2 1980 115269774 Power N-CT47^2T3T2 1981 115383041 Power N-CT47^2Arc(2)T3 1982 115519381 Power N-CT47^2Trin1,2,2 1983 115632648 Power N-CT47^2Arc(3)T2 1984 115745915 Power N-CT47^2Arc(5) 2024 115820666 Power N-CT47^2T3T1 2025 115957006 Power N-CT47^2T2T2 2026 116070273 Power N-CT47^2Arc(2)T2 2027 116183540 Power N-CT47^2Arc(4) 2068 116258291 Power N-CT47^2T3 2070 116507898 Power N-CT47^2T2T1 2071 116621165 Power N-CT47^2Arc(3) 2115 116945523 Power N-CT47^2T2 2116 117058790 Power N-CT47^2T1T1 2162 117496415 Power N-CT47^2T1 2209 117934040 Power N-CT47^2 2210 118163192 Power N-CT47^2+1 2211 121230746 Power N-CT47^2+2 2212 121574362 Power N-CT47^2+3 2239 123533620 Power N-CT53^2Arc(12) 2281 124071269 Power N-CT53^2Arc(11) 2324 124608918 Power N-CT53^2Arc(10) 2368 125146567 Power N-CT53^2Arc(9) 2413 125684216 Power N-CT53^2Arc(8) 2459 126221865 Power N-CT53^2Arc(7) 2506 126759514 Power N-CT53^2Arc(6) 2554 127297163 Power N-CT53^2Arc(5) 2603 127834812 Power N-CT53^2Arc(4) 2653 128372461 Power N-CT53^2Arc(3) 2916 128786189 Power CT31^3T22T13T13 3240 128974417 Power CT31^3T21T13T13 3564 129203793 Power CT31^3T20T13T13 3888 129433169 Power CT31^3T19T13T13 4096 129639181 Power CT31^3T15T15T15 4212 129662545 Power CT31^3T18T13T13 4608 129671437 Power CT31^3T15T15T13 5184 129703693 Power CT31^3T15T13T13 5832 129735949 Power CT31^3T13T13T13 6156 130194253 Power CT31^3T13T13T12 6480 130543328 Power CT31^3T13T13T11 6498 130652557 Power CT31^3T13T12T12 6804 130997069 Power CT31^3T13T13T10 6840 131001632 Power CT31^3T13T12T11 6859 131110861 Power CT31^3T12T12T12 7128 131226445 Power CT31^3T13T13T9 7200 131350707 Power CT31^3T13T11T11 7776 131394893 Power CT31^3T13T13T7 8100 131448653 Power CT31^3T13T13T6 8424 131455821 Power CT31^3T13T13T5 8550 131906957 Power CT31^3T13T12T6 8892 131914125 Power CT31^3T13T12T5 9000 132256032 Power CT31^3T13T11T6 9360 132263200 Power CT31^3T13T11T5 9386 132372429 Power CT31^3T12T12T5 9450 132709773 Power CT31^3T13T10T6 9500 132714336 Power CT31^3T12T11T6 9828 132716941 Power CT31^3T13T10T5 9880 132721504 Power CT31^3T12T11T5 9900 132939149 Power CT31^3T13T9T6 10000 132946317 Power CT31^3T13T9T5

Graph: