Table for CAN(6,k,21) 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,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 104648405 Augment OA 9 115485066 Augment OA 10 127301940 Augment OA 11 140142906 Augment OA 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 33 709917610 Martirosyan-TVT variant 34 710684658 Martirosyan-TVT 35 710805128 Martirosyan-TVT variant 36 710925698 Martirosyan-TVT 37 711070382 Martirosyan-TVT variant 38 711774884 Martirosyan-TVT 39 711919712 Martirosyan-TVT variant 40 712064684 Martirosyan-TVT 41 712185494 Martirosyan-TVT variant 42 712866078 Martirosyan-TVT 43 712950715 Martirosyan-TVT variant 44 713035401 Martirosyan-TVT 45 713265263 Martirosyan-TVT variant 46 714055160 Martirosyan-TVT 47 714333851 Martirosyan-TVT variant 48 715732419 Martirosyan-TVT 49 975615766 Martirosyan-TVT variant 50 1084946773 Martirosyan-TVT 51 1085626636 Martirosyan-TVT variant 52 1088652137 Martirosyan-TVT 53 1453481245 Martirosyan-TVT variant 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 1837058289 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 2325186664 Power CT23^2T15 207 2336023325 Power CT23^2T14 230 2347840199 Power CT23^2T13 253 2360681165 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 534 3541726632 Add 5 factors 535 3541939903 Add 5 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 4672237456 Add 1 factors 628 4947783076 Add 2 factors 629 5134114396 Add 3 factors 630 5259902550 Add 5 factors 631 5343034567 Add 5 factors 632 5455330797 Add 6 factors 648 5632467099 Add 23 factors 649 5732831426 Add 23 factors 651 5768888036 Power CT27^2Arc(3) 676 5912167896 Power CT27^2T1T1 702 6055447756 Power CT27^2T1 730 6198727616 Power CT27^2+1 769 6906699508 Martirosyan-TVT variant 865 6909423850 Martirosyan-TVT variant 961 6912148192 Martirosyan-TVT variant 1057 6914872534 Martirosyan-TVT variant 1058 6917596876 Martirosyan-TVT 1059 6941350385 Martirosyan-TVT variant 1060 6965103625 Martirosyan-TVT 1062 7741579045 Martirosyan-TVT 1064 8129032825 Martirosyan-TVT 1066 8388340825 Martirosyan-TVT 1068 8683396133 Martirosyan-TVT 1070 8691018204 Martirosyan-TVT 1104 8875876381 Martirosyan-TVT 1105 8887753981 Martirosyan-TVT variant 1106 8902428639 Martirosyan-TVT 1107 9233280979 Martirosyan-TVT variant 1128 9434375934 Power N-CT47^2T23 1152 9452015829 Martirosyan-TVT 1170 9529412078 Power N-CT47^2T21T2 1171 9529923284 Power N-CT47^2Arc(2)T21 1196 9530201975 Power N-CT47^2T21T1 1222 9530480666 Power N-CT47^2T21 1234 9672413247 Power N-CT47^2Trin1,2,19 1260 9672691938 Power N-CT47^2T19T2 1261 9673203144 Power N-CT47^2Arc(2)T19 1288 9673481835 Power N-CT47^2T19T1 1316 9673760526 Power N-CT47^2T19 1333 9860502764 Power N-CT43^2T12 1337 9876346356 Power N-CT47^2Trin2,2,16 1366 9877136253 Power N-CT47^2Trin1,2,16 1395 9877414944 Power N-CT47^2T16T2 1396 9877926150 Power N-CT47^2Arc(2)T16 1426 9878204841 Power N-CT47^2T16T1 1457 9878483532 Power N-CT47^2T16 1476 9969337106 Power N-CT41^2T5 1480 9969360980 Power N-CT41^2T4T1 1517 9969481790 Power N-CT41^2T4 1521 9970065338 Power N-CT41^2T2T2 1522 9970089500 Power N-CT41^2Arc(2)T2 1523 9970113662 Power N-CT41^2Arc(4) 1558 9970186292 Power N-CT41^2T3 1560 9970210310 Power N-CT41^2T2T1 1561 9970234472 Power N-CT41^2Arc(3) 1599 9970331120 Power N-CT41^2T2 1600 9970355282 Power N-CT41^2T1T1 1640 9970476092 Power N-CT41^2T1 1681 9970596902 Power N-CT41^2 1682 9980125078 Power N-CT41^2+1 1720 9980423965 Power N-CT43^2T3 1722 9980460138 Power N-CT43^2T2T1 1763 9980544775 Power N-CT43^2T2 1764 9981140722 Power N-CT43^2T1T1 1806 9981225359 Power N-CT43^2T1 1849 9981309996 Power N-CT43^2 1850 9982495600 Power N-CT43^2+1 1851 9985713668 Power N-CT43^2+2 1852 9996772226 Power N-CT43^2+3 1854 9997008412 Power N-CT47^2Trin2,3,3 1896 9997238274 Power N-CT47^2Trin2,2,3 1939 9997468136 Power N-CT47^2Trin2,2,2 1982 9998258033 Power N-CT47^2Trin1,2,2 2025 9998536724 Power N-CT47^2T2T2 2026 9999047930 Power N-CT47^2Arc(2)T2 2070 9999326621 Power N-CT47^2T2T1 2115 9999605312 Power N-CT47^2T2 2116 10000116518 Power N-CT47^2T1T1 2162 10000395209 Power N-CT47^2T1 2209 10000673900 Power N-CT47^2 2210 10020253852 Power N-CT47^2+1 2211 11155100572 Add 1 factors 2212 11575549972 Add 2 factors 2213 11828004832 Add 3 factors 2214 12034491985 Add 5 factors 2215 12054071937 Add 5 factors 2216 12215267986 Add 6 factors 2232 12558403206 Add 23 factors 2233 12577983158 Add 23 factors 2234 13279308500 Add 25 factors 2235 13298888452 Add 25 factors 2236 14385734138 Add 23 factors 2237 14592221291 Add 23 factors 2238 14611801243 Add 23 factors 2239 14772997292 Add 23 factors 2257 14830202199 Power CT49^2Arc(3) 2304 15090085546 Power CT49^2T1T1 2352 15349968893 Power CT49^2T1 2401 15609852240 Power CT49^2 2402 16751711280 Add 1 factors 4032 16961855384 Power CT31^3T24T7T7 4608 16980737668 Power CT31^3T23T7T7 5184 16991574329 Power CT31^3T22T7T7 5760 17003391203 Power CT31^3T21T7T7 6336 17016232169 Power CT31^3T20T7T7 10000 17024125148 Power CT31^3T13T7T7

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