Table for CAN(6,k,11) 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,11) 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 12 1771561 orthogonal array 13 3367430 extended OA (Colbourn) 14 4826805 orthogonal array fuse fuse 15 6588450 Add 2 factors 16 8198960 Add 3 factors 22 8213601 double OA (Colbourn-Zhou) 24 8373321 double OA (Colbourn-Zhou) 25 11593131 Add 1 factors 26 14667741 Add 2 factors 27 17329741 Add 3 factors 28 18940251 Add 4 factors 29 20005051 Add 11 factors 30 20084911 Add 11 factors 31 20098221 Add 11 factors 32 20204701 Add 11 factors 33 20284561 Add 11 factors 34 20444281 Add 11 factors 35 20550761 Add 11 factors 36 25261401 Add 11 factors 37 30080721 Add 11 factors 38 31386388 Martirosyan-Tran van Trung 40 31854724 Martirosyan-Tran van Trung 44 32205976 Martirosyan-Tran van Trung 46 32834032 Martirosyan-Tran van Trung 48 38364798 Martirosyan-Tran van Trung 49 40745880 perfect hash family23,49,12 50 42517440 perfect hash family24,50,12 52 44289000 perfect hash family25,52,12 55 46060560 perfect hash family26,55,12 59 47832120 perfect hash family27,59,12 60 52282995 perfect hash family16,65,13T1 65 53878864 perfect hash family16,65,13 66 61478874 Add 1 factors 67 64698684 Add 2 factors 70 64947570 Add 11 factors 71 69398445 Add 11 factors 76 70994314 Add 11 factors 77 78594324 Add 11 factors 78 81814134 Add 11 factors 81 82063020 Add 11 factors 82 86513895 Add 11 factors 88 87257929 Martirosyan-Tran van Trung 90 87886875 Martirosyan-Tran van Trung 92 89496385 Martirosyan-Tran van Trung 96 95027151 Martirosyan-Tran van Trung 98 97408233 Martirosyan-Tran van Trung 100 99179793 Martirosyan-Tran van Trung 112 100833949 Power CT16^2Arc(18):9 twos,0 ones 113 104357239 Power CT16^2Arc(18):7 twos,2 ones 118 104547593 Martirosyan-Tran van Trung 120 105415184 Power CT16^2Arc(16) 121 107025694 Power CT16^2Arc(15) 123 108636204 Power CT16^2Arc(14) 126 110246714 Power CT16^2Arc(13) 130 110594337 Martirosyan-Tran van Trung 131 112863194 Power CT16^2Arc(14):4 twos,3 ones 132 113014329 Power CT16^2Arc(16):3 twos,5 ones 133 113165464 Power CT16^2Arc(18):2 twos,7 ones 135 113467734 Power CT16^2Arc(11) 136 114322569 Power CT16^2TD(4):2,2,2,2,2 137 114473704 Power CT16^2Arc(12):4 twos,2 ones 138 114624839 Power CT16^2Arc(14):3 twos,4 ones 139 114775974 Power CT16^2Arc(16):2 twos,6 ones 140 114927109 Power CT16^2Arc(18):1 twos,8 ones 141 115078244 Power CT16^2Arc(10) 144 116084214 Power CT16^2TD(4):2,2,2,2,1 145 116235349 Power CT16^2Arc(12):3 twos,3 ones 146 116386484 Power CT16^2Arc(14):2 twos,5 ones 147 116537619 Power CT16^2Arc(16):1 twos,7 ones 148 116688754 Power CT16^2Arc(9) 152 117694724 Power CT16^2TD(4):2,2,2,2,0 153 117845859 Power CT16^2TD(4):2,2,2,1,1 154 117996994 Power CT16^2Arc(12):2 twos,4 ones 155 118148129 Power CT16^2Arc(14):1 twos,6 ones 156 118299264 Power CT16^2Arc(8) 162 119456369 Power CT16^2TD(4):2,2,2,1,0 163 119607504 Power CT16^2TD(4):2,2,1,1,1 164 119758639 Power CT16^2Arc(5)T2 165 119909774 Power CT16^2Arc(7) 172 121066879 Power CT16^2TD(2):2,2,2 173 121218014 Power CT16^2TD(4):2,2,1,1,0 174 121369149 Power CT16^2Arc(4)T2 175 121520284 Power CT16^2Arc(6) 184 122828524 Power CT16^2TD(2):1,2,2 185 122979659 Power CT16^2Arc(3)T2 186 123130794 Power CT16^2Arc(5) 196 124439034 Power CT16^2T2T2 197 124590169 Power CT16^2Arc(2)T2 198 124741304 Power CT16^2Arc(4) 228 124975560 Power CT19^2T7 247 126571429 Power CT19^2T6 253 127051920 Power CT23^2Arc(2)T11 264 127211640 Power CT23^2T11T1 276 127371360 Power CT23^2T11 286 128807509 Power CT23^2T10T1 299 128967229 Power CT23^2T10 308 130266884 Power CT23^2T9T1 322 130426604 Power CT23^2T9 364 131417600 Power CT19^2+3 373 132695360 Power CT23^2Arc(8) 389 132855080 Power CT23^2Arc(7) 406 133014800 Power CT23^2Arc(6) 424 133174520 Power CT23^2Arc(5) 443 133334240 Power CT23^2Arc(4) 463 133493960 Power CT23^2Arc(3) 484 133653680 Power CT23^2T1T1 506 133813400 Power CT23^2T1 530 133973120 Power CT23^2+1 531 150345630 Add 1 factors 532 157812540 Add 2 factors 533 162351250 Add 3 factors 534 163961760 Add 4 factors 541 165572270 Add 11 factors 553 175830650 Power CT25^2Arc(3) 576 179050460 Power CT25^2T1T1 600 182270270 Power CT25^2T1 625 185490080 Power CT25^2 626 201873590 Add 1 factors 627 209352600 Add 2 factors 628 213891310 Add 3 factors 629 215501820 Add 4 factors 636 217112330 Add 11 factors 637 233495840 Add 11 factors 638 238475636 Add 13 factors 639 245513560 Add 11 factors 640 247124070 Add 11 factors 647 248734580 Add 11 factors 648 265118090 Add 11 factors 650 268877230 Power CT27^2T2T1 651 269289840 Power CT27^2Arc(3) 675 271539230 Power CT27^2T2 676 271951840 Power CT27^2T1T1 702 274613840 Power CT27^2T1 729 277275840 Power CT27^2 744 289748400 Power N-CT31^2T7 750 292954900 Power N-CT31^2T6T1 775 292968210 Power N-CT31^2T6 780 296029510 Power N-CT31^2T5T1 806 296042820 Power N-CT31^2T5 810 298691510 Power N-CT31^2T4T1 837 298704820 Power N-CT31^2T4 841 300075750 Power N-CT29^2 868 300315330 Power N-CT31^2T3 870 301366820 Power N-CT31^2T2T1 899 301380130 Power N-CT31^2T2 900 301446680 Power N-CT31^2T1T1 930 301459990 Power N-CT31^2T1 961 301473300 Power N-CT31^2 962 303070500 Power N-CT31^2+1 963 304268400 Power N-CT31^2+2 964 306664200 Power N-CT31^2+3 965 323047710 Add 1 factors 992 323168720 Power CT32^2T1 1024 323275200 Power CT32^2 1025 324552960 Power CT32^2+1 1026 327108480 Power CT32^2+2 1027 328812160 Power CT32^2+3 1060 336520123 Martirosyan-Tran van Trung 1061 352903633 Add 1 factors 1062 359680733 Martirosyan-Tran van Trung 1063 364921353 Add 3 factors 1064 366531863 Add 4 factors 1071 368142373 Add 11 factors 1082 381961673 Martirosyan-Tran van Trung 1083 398345183 Add 1 factors 1084 399008153 Martirosyan-Tran van Trung 1086 401247253 Martirosyan-Tran van Trung 1088 404598353 Martirosyan-Tran van Trung 1100 406062453 Martirosyan-Tran van Trung 1104 406254173 Martirosyan-Tran van Trung 1106 407225793 Martirosyan-Tran van Trung 1152 413240703 Martirosyan-Tran van Trung 1200 419255613 Martirosyan-Tran van Trung 1250 425270523 Martirosyan-Tran van Trung 1260 432283860 Power N-CT41^2T6T5 1265 436643248 Power N-CT41^2Trin1,5,5 1296 436994500 Power N-CT41^2T5T5 1301 437823427 Power N-CT41^2Arc(4)T6 1333 438174679 Power N-CT41^2Arc(3)T6 1366 438525931 Power N-CT41^2Arc(2)T6 1400 438877183 Power N-CT41^2T6T1 1419 438962235 Power N-CT43^2T10 1462 439121955 Power N-CT43^2T9 1505 439228435 Power N-CT43^2T8 1548 443939075 Power N-CT43^2T7 1591 448758395 Power N-CT43^2T6 1634 450064062 Power N-CT43^2T5 1720 450532398 Power N-CT43^2T3 1850 450883650 Power N-CT43^2+1 1852 459676434 Power N-CT43^2+3 1853 483061664 Add 1 factors 1854 490450210 Add 4 factors 1860 491771530 Add 11 factors 1861 492060720 Add 11 factors 1901 498391796 Power N-CT47^2Arc(7) 1942 503922562 Power N-CT47^2Arc(6) 1984 509453328 Power N-CT47^2Arc(5) 2027 514984094 Power N-CT47^2Arc(4) 2071 520514860 Power N-CT47^2Arc(3) 2116 526045626 Power N-CT47^2T1T1 2162 531576392 Power N-CT47^2T1 2210 537107158 Power N-CT47^2+1 2211 561769928 Add 1 factors 2212 571931508 Add 2 factors 2352 574175328 Power CT31^3T19T17T17 2366 574311822 Power CT31^3T18T18T17 3168 574506880 Power CT31^3T19T19T9 3456 574666600 Power CT31^3T19T19T7 3744 576262469 Power CT31^3T19T18T7 4032 577721844 Power CT31^3T19T17T7 4056 577858338 Power CT31^3T18T18T7 4368 579317713 Power CT31^3T18T17T7 4704 580777088 Power CT31^3T17T17T7 5808 580948920 Power CT31^3T19T9T9 6336 581108640 Power CT31^3T19T9T7 6912 581268360 Power CT31^3T19T7T7 7488 582864229 Power CT31^3T18T7T7 8064 584323604 Power CT31^3T17T7T7 8640 586085249 Power CT31^3T16T7T7 10000 587390960 Power CT31^3T10T9T9

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