Table for CAN(6,k,21) 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,21) 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 85766121 composition 8 104772459 Add a symbol 9 115801137 Add a symbol 10 127990730 Add a symbol 11 141463438 Add a symbol 24 148035885 orthogonal array fuse fuse 26 244140617 orthogonal array fuse fuse fuse fuse 28 387420477 orthogonal array fuse fuse fuse fuse fuse fuse 31 592143483 perfect hash family4,31,23,c fuse fuse 32 688248268 perfect hash family4,35,25S3 34 710684658 Martirosyan-Tran van Trung 36 710925698 Martirosyan-Tran van Trung 38 711774884 Martirosyan-Tran van Trung 40 712064684 Martirosyan-Tran van Trung 42 712866078 Martirosyan-Tran van Trung 44 713035401 Martirosyan-Tran van Trung 46 714055160 Martirosyan-Tran van Trung 48 715732419 Martirosyan-Tran van Trung 49 1017477639 Add 1 factors 50 1086092380 Martirosyan-Tran van Trung 52 1088652137 Martirosyan-Tran van Trung 53 1464611357 Add 1 factors 54 1480358679 perfect hash family10,54,23,c fuse fuse 55 1480358840 perfect hash family10,55,24 63 1628394545 perfect hash family11,63,23,c fuse fuse 64 1628394724 perfect hash family11,64,24 67 1776430411 perfect hash family12,67,23,c fuse fuse 68 1776430608 perfect hash family12,68,24 69 1836779598 Add 23 factors 70 1838456857 Add 23 factors 71 1839422811 Add 23 factors 72 2072502376 perfect hash family14,72,24 115 2220538009 perfect hash family15,115,23,c fuse fuse 161 2306304380 Power CT23^2T16 184 2325310718 Power CT23^2T15 207 2336339396 Power CT23^2T14 230 2348528989 Power CT23^2T13 253 2362001697 Power CT23^2T12 529 2368573875 perfect hash family16,529,23,c fuse fuse 530 2368574144 Power CT23^2+1 531 2940685964 Add 1 factors 532 3155267744 Add 2 factors 533 3336783344 Add 3 factors 553 3617935660 Power CT25^2Arc(3) 576 3714040392 Power CT25^2T1T1 600 3810145124 Power CT25^2T1 625 3906249617 perfect hash family16,625,25,c fuse fuse fuse fuse 626 3906249856 Power CT25^2+1 627 4673018656 Add 1 factors 628 4948564276 Add 2 factors 629 5134895596 Add 3 factors 630 5570197331 Add 5 factors 648 5632467099 Add 23 factors 649 5733772586 Add 23 factors 651 5768888036 Power CT27^2Arc(3) 676 5912167896 Power CT27^2T1T1 702 6055447756 Power CT27^2T1 730 6198727616 Power CT27^2+1 768 6906699508 Martirosyan-Tran van Trung 864 6909423850 Martirosyan-Tran van Trung 960 6912148192 Martirosyan-Tran van Trung 1056 6914872534 Martirosyan-Tran van Trung 1058 6917596876 Martirosyan-Tran van Trung 1060 6965103625 Martirosyan-Tran van Trung 1062 7741579045 Martirosyan-Tran van Trung 1064 8129032825 Martirosyan-Tran van Trung 1066 8388340825 Martirosyan-Tran van Trung 1068 8873856741 Martirosyan-Tran van Trung 1104 8875876381 Martirosyan-Tran van Trung 1106 8902428639 Martirosyan-Tran van Trung 1152 9452015829 Martirosyan-Tran van Trung 1171 9545307532 Power N-CT47^2Arc(2)T21 1196 9546984791 Power N-CT47^2T21T1 1222 9548662050 Power N-CT47^2T21 1235 9686910133 Power N-CT47^2Arc(3)T19 1261 9688587392 Power N-CT47^2Arc(2)T19 1288 9690264651 Power N-CT47^2T19T1 1316 9691941910 Power N-CT47^2T19 1333 9861603682 Power N-CT43^2T12 1339 9889955880 Power N-CT47^2Arc(4)T16 1367 9891633139 Power N-CT47^2Arc(3)T16 1396 9893310398 Power N-CT47^2Arc(2)T16 1426 9894987657 Power N-CT47^2T16T1 1457 9896664916 Power N-CT47^2T16 1486 9976118108 Power N-CT41^2Arc(5) 1523 9976919502 Power N-CT41^2Arc(4) 1561 9977720896 Power N-CT41^2Arc(3) 1600 9978522290 Power N-CT41^2T1T1 1640 9979323684 Power N-CT41^2T1 1682 9980125078 Power N-CT41^2+1 1720 9981524883 Power N-CT43^2T3 1723 9981987631 Power N-CT43^2Arc(3) 1764 9982156954 Power N-CT43^2T1T1 1806 9982326277 Power N-CT43^2T1 1850 9982495600 Power N-CT43^2+1 1852 9996772226 Power N-CT43^2+3 1861 10006835780 Power N-CT47^2Arc(8) 1901 10008513039 Power N-CT47^2Arc(7) 1942 10010190298 Power N-CT47^2Arc(6) 1984 10011867557 Power N-CT47^2Arc(5) 2027 10013544816 Power N-CT47^2Arc(4) 2071 10015222075 Power N-CT47^2Arc(3) 2116 10016899334 Power N-CT47^2T1T1 2162 10018576593 Power N-CT47^2T1 2210 10020253852 Power N-CT47^2+1 2211 11155100572 Add 1 factors 2212 11575549972 Add 2 factors 2213 11828004832 Add 3 factors 2214 12436383612 Add 4 factors 2215 12515713390 Add 5 factors 2233 12577983158 Add 23 factors 2235 13298888452 Add 25 factors 2236 14385734138 Add 23 factors 2237 14854184572 Add 25 factors 2238 15073442696 Add 23 factors 2239 15135712464 Add 23 factors 2244 15135934598 Add 23 factors 2254 15135936116 Add 23 factors 2256 15138414504 Add 23 factors 2257 15374406548 Power CT49^2Arc(3) 2304 15676151768 Power CT49^2T1T1 2352 15977896988 Power CT49^2T1 2401 16279642208 Power CT49^2 4032 16961855384 Power CT31^3T24T7T7 4608 16980861722 Power CT31^3T23T7T7 5184 16991890400 Power CT31^3T22T7T7 5760 17004079993 Power CT31^3T21T7T7 6336 17017552701 Power CT31^3T20T7T7 10000 17024125148 Power CT31^3T13T7T7

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