Table for CAN(6,k,21) for k up to 10000

Last Updated Tue Jan 31 05:20:10 MST 2012

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 36 712958330 Martirosyan-Tran van Trung 40 713518004 Martirosyan-Tran van Trung 44 714077678 Martirosyan-Tran van Trung 46 714434069 double OA (Colbourn-Zhou) fuse fuse 48 715756700 Martirosyan-Tran van Trung 49 985259360 Add a factor 50 1086524588 Martirosyan-Tran van Trung 52 1088868290 Martirosyan-Tran van Trung 53 1461352430 Add a factor 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 1924466492 perfect hash family13,69,24 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 a factor 532 3605900444 Add a factor 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 4706608996 Add a factor 628 5546413276 Add a factor 651 5768888036 Power CT27^2Arc(3) 676 5912167896 Power CT27^2T1T1 702 6055447756 Power CT27^2T1 730 6198727616 Power CT27^2+1 731 7123447496 Add a factor 735 7253757453 perfect hash family49,735,23,c fuse fuse 768 7569163156 Martirosyan-Tran van Trung 864 7571887498 Martirosyan-Tran van Trung 960 7574611840 Martirosyan-Tran van Trung 1056 7577336182 Martirosyan-Tran van Trung 1058 7580060524 Martirosyan-Tran van Trung 1060 8014539873 Martirosyan-Tran van Trung 1062 8884154493 Martirosyan-Tran van Trung 1081 9450227709 Power N-CT47^2Arc(2)T23 1104 9451550340 Power N-CT47^2T23T1 1128 9452872971 Power N-CT47^2T23 1147 9545009810 Power N-CT47^2Arc(3)T21 1171 9546332441 Power N-CT47^2Arc(2)T21 1196 9547655072 Power N-CT47^2T21T1 1222 9548977703 Power N-CT47^2T21 1235 9688289670 Power N-CT47^2Arc(3)T19 1261 9689612301 Power N-CT47^2Arc(2)T19 1288 9690934932 Power N-CT47^2T19T1 1316 9692257563 Power N-CT47^2T19 1333 9875153283 Power N-CT43^2T12 1339 9891690045 Power N-CT47^2Arc(4)T16 1367 9893012676 Power N-CT47^2Arc(3)T16 1396 9894335307 Power N-CT47^2Arc(2)T16 1426 9895657938 Power N-CT47^2T16T1 1457 9896980569 Power N-CT47^2T16 1472 9991762723 Power N-CT47^2T15T1 1504 9993085354 Power N-CT47^2T15 1523 9994848782 Power N-CT41^2Arc(4) 1561 9995408456 Power N-CT41^2Arc(3) 1600 9995968130 Power N-CT41^2T1T1 1720 9996527804 Power N-CT43^2T3 1850 9997087478 Power N-CT43^2+1 1852 10002076952 Power N-CT43^2+3 1861 10010012738 Power N-CT47^2Arc(8) 1901 10011335369 Power N-CT47^2Arc(7) 1942 10012658000 Power N-CT47^2Arc(6) 1984 10013980631 Power N-CT47^2Arc(5) 2027 10015303262 Power N-CT47^2Arc(4) 2071 10016625893 Power N-CT47^2Arc(3) 2116 10017948524 Power N-CT47^2T1T1 2162 10019271155 Power N-CT47^2T1 2210 10020593786 Power N-CT47^2+1 2211 11278947386 Add a factor 2212 12537300986 Add a factor 2213 13795654586 Add a factor 2257 14955641764 Power CT49^2Arc(3) 2304 15225144424 Power CT49^2T1T1 2352 15494647084 Power CT49^2T1 2401 15764149744 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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