Table for CAN(6,k,10) 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,10) 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 1000000 composition 8 1229001 Augment OA 9 1357802 Augment OA 10 1494326 Augment OA 12 1771559 orthogonal array fuse 13 2928200 extended OA (Colbourn) special fuse 14 4233419 Add 2 factors 15 5407880 Add 2 factors 16 6982867 Martirosyan-TVT 17 7286858 Martirosyan-TVT variant 18 7357468 Martirosyan-TVT 19 7626855 Martirosyan-TVT variant 20 7694096 Martirosyan-TVT 21 8105506 Martirosyan-TVT variant 22 8213599 double OA (Colbourn-Zhou) fuse 23 8250640 Martirosyan-TVT variant 24 8303705 Martirosyan-TVT 25 10922705 Add 1 factors 26 13036805 Add 2 factors 27 15829565 Add 3 factors 28 16572762 Martirosyan-TVT 29 17581073 Add 5 factors 30 18445644 Add 6 factors 31 18693876 Add 11 factors 32 19120906 Add 11 factors 33 19458679 Add 11 factors 34 19559080 Add 11 factors 35 19697615 Add 11 factors 36 23207505 Add 11 factors 37 26264142 Martirosyan-TVT variant 38 26617803 Martirosyan-TVT 39 26728924 Martirosyan-TVT variant 40 26750934 Martirosyan-TVT 41 27515707 Martirosyan-TVT variant 42 28162355 Martirosyan-TVT 43 28365740 Martirosyan-TVT variant 44 28613212 Martirosyan-TVT 45 28716053 Martirosyan-TVT variant 46 29042404 Martirosyan-TVT 47 30366251 Martirosyan-TVT variant 48 32115271 Martirosyan-TVT 49 37384051 Add 1 factors 50 39751051 Add 2 factors 51 41740480 Add 5 factors 52 42758077 Add 11 factors 53 43484035 Add 11 factors 54 43687420 Add 11 factors 55 43934892 Add 11 factors 56 44037733 Add 11 factors 57 44364084 Add 11 factors 60 45694543 perfect hash family16,65,13T1 65 46851184 perfect hash family16,65,13 66 52456834 Add 1 factors 67 54849934 Add 2 factors 68 56583882 Martirosyan-TVT 70 56722417 Martirosyan-TVT 72 60232307 Martirosyan-TVT 76 62683154 Add 11 factors 77 68288804 Add 11 factors 78 68774612 Martirosyan-TVT 79 68892211 Martirosyan-TVT variant 80 69007183 Martirosyan-TVT 81 69916156 Martirosyan-TVT variant 82 70060356 Martirosyan-TVT 84 70715995 Martirosyan-TVT 86 70939549 Martirosyan-TVT 88 71253450 Martirosyan-TVT 90 71365282 Martirosyan-TVT 91 71767624 Martirosyan-TVT variant 92 71834624 Martirosyan-TVT 94 73178640 Martirosyan-TVT 96 74927660 Martirosyan-TVT 98 80262869 Martirosyan-TVT 99 82638860 Martirosyan-TVT variant 100 82873028 Martirosyan-TVT 101 85118610 Martirosyan-TVT variant 102 85366613 Martirosyan-TVT 104 86404379 Martirosyan-TVT 120 86526064 Power CT16^2Arc(16) 121 88101051 Power CT16^2Arc(15) 123 89676038 Power CT16^2Arc(14) 126 91251025 Power CT16^2Arc(13) 128 91856865 Martirosyan-TVT 130 91961445 Martirosyan-TVT 135 94400999 Power CT16^2Arc(11) 141 95975986 Power CT16^2Arc(10) 148 97550973 Power CT16^2Arc(9) 156 99125960 Power CT16^2Arc(8) 165 100700947 Power CT16^2Arc(7) 175 102275934 Power CT16^2Arc(6) 186 103850921 Power CT16^2Arc(5) 198 105425908 Power CT16^2Arc(4) 211 107000895 Power CT16^2Arc(3) 225 108575882 Power CT16^2T1T1 240 110150869 Power CT16^2T1 256 111725856 Power CT16^2 272 116285721 Power CT17^2T1 289 116589712 Power CT17^2 290 117719472 Power CT17^2+1 291 120952116 Power CT19^2Arc(4) 307 121221503 Power CT19^2Arc(3) 324 121490890 Power CT19^2T1T1 342 121760277 Power CT19^2T1 361 122029664 Power CT19^2 362 123105520 Power CT19^2+1 363 129688080 Power CT19^2+2 368 130742451 Power CT23^2T7 380 130829895 Power CT23^2T4T3 383 130860095 Power CT23^2Trin1,3,3 400 130897136 Power CT23^2T3T3 414 131117052 Power CT23^2T5 420 131308546 Power CT23^2T3T2 421 131379598 Power CT23^2Arc(2)T3 437 131386439 Power CT23^2T4 440 131416639 Power CT23^2T3T1 460 131453680 Power CT23^2T3 462 131828049 Power CT23^2T2T1 483 131865090 Power CT23^2T2 484 131936142 Power CT23^2T1T1 506 131973183 Power CT23^2T1 529 132010224 Power CT23^2 530 132859264 Power CT23^2+1 531 145452244 Add 1 factors 532 150321244 Add 2 factors 534 156722045 Add 5 factors 535 157571085 Add 5 factors 536 159900911 Add 6 factors 537 160935054 Add 11 factors 540 161015354 Add 11 factors 541 161864394 Add 11 factors 553 166906264 Power CT25^2Arc(3) 576 169525264 Power CT25^2T1T1 600 172144264 Power CT25^2T1 625 174763264 Power CT25^2 626 187519414 Add 1 factors 627 192679114 Add 2 factors 628 199909384 Add 3 factors 630 200026209 Add 5 factors 631 202411293 Add 6 factors 636 204385274 Add 11 factors 637 217141424 Add 11 factors 638 222301124 Add 11 factors 639 229531394 Add 11 factors 641 229648219 Add 11 factors 642 232033303 Add 11 factors 647 234007284 Add 11 factors 651 244894744 Power CT27^2Arc(3) 676 247687504 Power CT27^2T1T1 702 250480264 Power CT27^2T1 729 253273024 Power CT27^2 754 259171812 Power N-CT29^2T3 757 260691147 Power N-CT29^2Arc(3) 784 261699458 Power N-CT29^2T1T1 812 262707769 Power N-CT29^2T1 841 263716080 Power N-CT29^2 842 276684645 Power N-CT29^2+1 868 278287011 Power N-CT31^2T3 870 279047090 Power N-CT31^2T2T1 899 279295322 Power N-CT31^2T2 900 279911661 Power N-CT31^2T1T1 930 280159893 Power N-CT31^2T1 961 280408125 Power N-CT31^2 962 286813575 Power N-CT31^2+1 963 291880170 Power N-CT31^2+2 964 293386185 Power N-CT31^2+3 966 295569724 Martirosyan-TVT 968 295690546 Martirosyan-TVT 1012 295758205 Martirosyan-TVT 1030 295825864 Martirosyan-TVT 1031 295855864 Martirosyan-TVT variant 1040 295885864 Martirosyan-TVT 1041 295886464 Martirosyan-TVT variant 1044 295887064 Martirosyan-TVT 1045 296929064 Martirosyan-TVT variant 1050 298011064 Martirosyan-TVT 1051 298230064 Martirosyan-TVT variant 1058 298449064 Martirosyan-TVT 1060 299605004 Martirosyan-TVT 1061 313009514 Add 1 factors 1062 316580084 Martirosyan-TVT 1064 323879084 Martirosyan-TVT 1065 326082516 Add 5 factors 1066 328583325 Add 6 factors 1069 329449154 Add 11 factors 1071 330605094 Add 11 factors 1072 337538241 Martirosyan-TVT 1074 338572384 Martirosyan-TVT 1080 338652684 Martirosyan-TVT 1081 339859024 Martirosyan-TVT variant 1082 339909424 Martirosyan-TVT 1084 349333394 Martirosyan-TVT 1085 352878281 Martirosyan-TVT variant 1098 354591281 Martirosyan-TVT 1104 354851201 Martirosyan-TVT 1106 355438613 Martirosyan-TVT 1130 358057613 Martirosyan-TVT 1131 358166513 Martirosyan-TVT variant 1144 358275413 Martirosyan-TVT 1145 358406743 Martirosyan-TVT variant 1146 358538602 Martirosyan-TVT 1152 358798522 Martirosyan-TVT 1154 364390960 Martirosyan-TVT 1156 364455940 Martirosyan-TVT 1177 364585900 Martirosyan-TVT variant 1198 364867006 Martirosyan-TVT 1200 365061946 Martirosyan-TVT 1201 367967197 Martirosyan-TVT variant 1209 368253448 Martirosyan-TVT variant 1210 368536456 Martirosyan-TVT 1211 368671198 Martirosyan-TVT variant 1212 368740960 Martirosyan-TVT 1224 368748898 Martirosyan-TVT 1236 368749060 Martirosyan-TVT 1248 368846602 Martirosyan-TVT 1250 369968704 Martirosyan-TVT 1260 373093590 Power N-CT41^2T6T5 1270 373577927 Power N-CT41^2Arc(5)T6 1301 374342700 Power N-CT41^2Arc(4)T6 1333 375107473 Power N-CT41^2Arc(3)T6 1366 375872246 Power N-CT41^2Arc(2)T6 1400 376637019 Power N-CT41^2T6T1 1435 377401792 Power N-CT41^2T6 1440 380146909 Power N-CT41^2T5T1 1450 380631246 Power N-CT41^2Arc(6) 1476 380911682 Power N-CT41^2T5 1486 381396019 Power N-CT41^2Arc(5) 1523 382160792 Power N-CT41^2Arc(4) 1561 382925565 Power N-CT41^2Arc(3) 1600 383690338 Power N-CT41^2T1T1 1640 384455111 Power N-CT41^2T1 1681 385219884 Power N-CT41^2 1682 394272956 Power N-CT41^2+1 1720 395505540 Power N-CT43^2T3 1722 396066928 Power N-CT43^2T2T1 1763 396270313 Power N-CT43^2T2 1764 396713576 Power N-CT43^2T1T1 1806 396916961 Power N-CT43^2T1 1849 397120346 Power N-CT43^2 1850 400584954 Power N-CT43^2+1 1851 402024728 Power N-CT43^2+2 1852 406593642 Power N-CT43^2+3 1861 414536724 Power N-CT47^2Arc(8) 1901 415860571 Power N-CT47^2Arc(7) 1942 417184418 Power N-CT47^2Arc(6) 1984 418508265 Power N-CT47^2Arc(5) 2027 419832112 Power N-CT47^2Arc(4) 2071 421155959 Power N-CT47^2Arc(3) 2116 422479806 Power N-CT47^2T1T1 2162 423803653 Power N-CT47^2T1 2209 425127500 Power N-CT47^2 2210 444170870 Add 1 factors 2211 450925370 Add 2 factors 2214 459392843 Add 5 factors 2215 462641859 Add 6 factors 2220 465043860 Add 11 factors 2221 484087230 Add 11 factors 2222 490123652 Add 13 factors 2225 499309203 Add 11 factors 2226 502558219 Add 11 factors 2231 504960220 Add 11 factors 2232 524003590 Add 11 factors 2233 530040012 Add 13 factors 2366 533518316 Power CT31^3T18T18T17 2448 534258473 Power CT31^3T19T19T14 2592 534329083 Power CT31^3T19T19T13 2736 534598470 Power CT31^3T19T19T12 2880 534665711 Power CT31^3T19T19T11 3024 535077121 Power CT31^3T19T19T10 3168 535185214 Power CT31^3T19T19T9 3312 535222255 Power CT31^3T19T19T8 3456 535275320 Power CT31^3T19T19T7 3588 536378896 Power CT31^3T19T18T8 3744 536431961 Power CT31^3T19T18T7 3887 537535537 Power CT31^3T18T18T8 4056 537588602 Power CT31^3T18T18T7 4186 538840756 Power CT31^3T18T17T8 4368 538893821 Power CT31^3T18T17T7 4485 540015217 Power CT31^3T18T16T8 4680 540068282 Power CT31^3T18T16T7 4704 540199040 Power CT31^3T17T17T7 4800 540588248 Power CT31^3T19T11T11 4896 540790619 Power CT31^3T19T14T7 4968 540808164 Power CT31^3T19T13T8 5184 540861229 Power CT31^3T19T13T7 5244 541077551 Power CT31^3T19T12T8 5280 541107751 Power CT31^3T19T11T9 5472 541130616 Power CT31^3T19T12T7 5520 541144792 Power CT31^3T19T11T8 5760 541197857 Power CT31^3T19T11T7 5796 541556202 Power CT31^3T19T10T8 6048 541609267 Power CT31^3T19T10T7 6072 541664295 Power CT31^3T19T9T8 6348 541701336 Power CT31^3T19T8T8 6624 541754401 Power CT31^3T19T8T7 6912 541807466 Power CT31^3T19T7T7 7176 542911042 Power CT31^3T18T8T7 7488 542964107 Power CT31^3T18T7T7 7728 544216261 Power CT31^3T17T8T7 8064 544269326 Power CT31^3T17T7T7 8280 545390722 Power CT31^3T16T8T7 8640 545443787 Power CT31^3T16T7T7 8832 546965709 Power CT31^3T15T8T7 9216 547018774 Power CT31^3T15T7T7 9600 547120394 Power CT31^3T11T11T7 9792 547322765 Power CT31^3T14T7T7 9936 547340310 Power CT31^3T13T8T7 10000 547393375 Power CT31^3T13T7T7

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