Table for CAN(6,k,10) 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,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 1234567 Add a symbol 9 1371741 Add a symbol 10 1524156 Add a symbol 12 1771559 orthogonal array fuse 13 3070619 Add 1 factors 14 4234319 Add 2 factors 15 5551199 Add 2 factors 16 7030109 Martirosyan-Tran van Trung 18 7415333 Martirosyan-Tran van Trung 20 7731599 Martirosyan-Tran van Trung 22 8213599 double OA (Colbourn-Zhou) fuse 24 8308707 Martirosyan-Tran van Trung 25 10927707 Add 1 factors 26 13042707 Add 2 factors 27 15835777 Add 3 factors 28 17021259 Martirosyan-Tran van Trung 29 18260123 Add 11 factors 30 18618079 Add 11 factors 31 18731379 Add 11 factors 32 19228999 Add 11 factors 33 19459889 Add 11 factors 34 19618357 Add 11 factors 35 19703827 Add 11 factors 36 23214707 Add 11 factors 37 26412517 Add 2 factors 38 26751788 Martirosyan-Tran van Trung 40 26795808 Martirosyan-Tran van Trung 42 28361944 Martirosyan-Tran van Trung 44 28624320 Martirosyan-Tran van Trung 46 29140369 Martirosyan-Tran van Trung 48 32132685 Martirosyan-Tran van Trung 49 37401645 Add 1 factors 50 39768645 Add 2 factors 51 42025088 Add 11 factors 52 43604534 Add 11 factors 53 43683954 Add 11 factors 55 43946330 Add 11 factors 57 44462379 Add 11 factors 59 47491435 Add 11 factors 60 47830828 perfect hash family16,65,13T1 65 49129888 perfect hash family16,65,13 66 54739408 Add 1 factors 68 56957241 Martirosyan-Tran van Trung 70 57110031 Martirosyan-Tran van Trung 72 61516348 Martirosyan-Tran van Trung 76 64966588 Add 11 factors 78 70310705 Martirosyan-Tran van Trung 80 70425681 Martirosyan-Tran van Trung 84 72849174 Martirosyan-Tran van Trung 88 73111550 Martirosyan-Tran van Trung 90 73737579 Martirosyan-Tran van Trung 92 74422231 Martirosyan-Tran van Trung 96 77459421 Martirosyan-Tran van Trung 98 82753824 Martirosyan-Tran van Trung 100 85407443 Martirosyan-Tran van Trung 112 87319618 Power CT16^2Arc(18):9 twos,0 ones 120 88819168 Power CT16^2Arc(16) 121 90298078 Power CT16^2Arc(15) 123 91776988 Power CT16^2Arc(14) 126 93255898 Power CT16^2Arc(13) 130 94734808 Power CT16^2Arc(12) 135 96213718 Power CT16^2Arc(11) 141 97692628 Power CT16^2Arc(10) 148 99171538 Power CT16^2Arc(9) 156 100650448 Power CT16^2Arc(8) 165 102129358 Power CT16^2Arc(7) 175 103608268 Power CT16^2Arc(6) 186 105087178 Power CT16^2Arc(5) 198 106566088 Power CT16^2Arc(4) 211 108044998 Power CT16^2Arc(3) 225 109523908 Power CT16^2T1T1 240 111002818 Power CT16^2T1 256 112481728 Power CT16^2 272 118260088 Power CT17^2T1 290 118645312 Power CT17^2+1 291 122440504 Power CT19^2Arc(4) 307 122756770 Power CT19^2Arc(3) 324 123073036 Power CT19^2T1T1 342 123389302 Power CT19^2T1 362 123705568 Power CT19^2+1 364 131417568 Power CT19^2+3 367 131594864 Power CT23^2tTD:3,3,2 368 131660698 Power CT23^2T7 383 131689972 Power CT23^2Trin1,3,3 400 131785080 Power CT23^2T3T3 414 132045922 Power CT23^2T5 421 132171972 Power CT23^2Arc(2)T3 440 132267080 Power CT23^2T3T1 460 132362188 Power CT23^2T3 463 132653972 Power CT23^2Arc(3) 484 132749080 Power CT23^2T1T1 506 132844188 Power CT23^2T1 530 132939296 Power CT23^2+1 531 145532546 Add 1 factors 532 150401546 Add 2 factors 533 157478146 Add 3 factors 534 160334246 Add 4 factors 535 161173195 Add 5 factors 537 161864456 Add 11 factors 541 161944756 Add 11 factors 553 166986296 Power CT25^2Arc(3) 576 169605296 Power CT25^2T1T1 600 172224296 Power CT25^2T1 625 174843296 Power CT25^2 626 187600346 Add 1 factors 627 192760046 Add 2 factors 628 199990516 Add 3 factors 629 202855896 Add 4 factors 630 203694845 Add 5 factors 636 204466406 Add 11 factors 637 217223456 Add 11 factors 638 222383156 Add 11 factors 639 229613626 Add 11 factors 640 232479006 Add 11 factors 641 233317955 Add 11 factors 647 234089516 Add 11 factors 651 244993206 Power CT27^2Arc(3) 676 247786276 Power CT27^2T1T1 702 250579346 Power CT27^2T1 729 253372416 Power CT27^2 730 266386866 Add 1 factors 754 268684414 Power N-CT29^2T3 757 270185238 Power N-CT29^2Arc(3) 784 271424102 Power N-CT29^2T1T1 812 272662966 Power N-CT29^2T1 841 273901830 Power N-CT29^2 868 279260550 Power N-CT31^2T3 870 280386114 Power N-CT31^2T2T1 899 280499414 Power N-CT31^2T2 900 280744070 Power N-CT31^2T1T1 930 280857370 Power N-CT31^2T1 961 280970670 Power N-CT31^2 962 288434970 Power N-CT31^2+1 963 291898320 Power N-CT31^2+2 964 294275340 Power N-CT31^2+3 968 296799746 Martirosyan-Tran van Trung 1012 296954236 Martirosyan-Tran van Trung 1030 297108726 Martirosyan-Tran van Trung 1040 297168726 Martirosyan-Tran van Trung 1044 297169926 Martirosyan-Tran van Trung 1050 299293926 Martirosyan-Tran van Trung 1060 299731926 Martirosyan-Tran van Trung 1061 313136436 Add 1 factors 1062 316707276 Martirosyan-Tran van Trung 1064 324006276 Martirosyan-Tran van Trung 1065 329960455 Add 5 factors 1071 330732016 Add 11 factors 1074 339855576 Martirosyan-Tran van Trung 1080 339935876 Martirosyan-Tran van Trung 1082 340034876 Martirosyan-Tran van Trung 1084 349458516 Martirosyan-Tran van Trung 1086 355224516 Martirosyan-Tran van Trung 1088 357815616 Martirosyan-Tran van Trung 1106 357858879 Martirosyan-Tran van Trung 1130 362381379 Martirosyan-Tran van Trung 1144 362606379 Martirosyan-Tran van Trung 1152 362869568 Martirosyan-Tran van Trung 1176 367392068 Martirosyan-Tran van Trung 1200 367673198 Martirosyan-Tran van Trung 1208 372301499 Martirosyan-Tran van Trung 1210 372584507 Martirosyan-Tran van Trung 1212 372730071 Martirosyan-Tran van Trung 1224 372738009 Martirosyan-Tran van Trung 1228 372738171 Martirosyan-Tran van Trung 1236 372845406 Martirosyan-Tran van Trung 1248 372877968 Martirosyan-Tran van Trung 1250 372878292 Martirosyan-Tran van Trung 1255 378273570 Power N-CT41^2Arc(12) 1285 379839706 Power N-CT41^2Arc(11) 1316 381405842 Power N-CT41^2Arc(10) 1348 382971978 Power N-CT41^2Arc(9) 1381 384538114 Power N-CT41^2Arc(8) 1415 386104250 Power N-CT41^2Arc(7) 1450 387670386 Power N-CT41^2Arc(6) 1486 389236522 Power N-CT41^2Arc(5) 1523 390802658 Power N-CT41^2Arc(4) 1561 392368794 Power N-CT41^2Arc(3) 1600 393934930 Power N-CT41^2T1T1 1640 395501066 Power N-CT41^2T1 1682 397067202 Power N-CT41^2+1 1720 398911954 Power N-CT43^2T3 1723 399953338 Power N-CT43^2Arc(3) 1764 400215714 Power N-CT43^2T1T1 1806 400478090 Power N-CT43^2T1 1850 400740466 Power N-CT43^2+1 1852 407965152 Power N-CT43^2+3 1853 425016102 Add 1 factors 1861 425919048 Power N-CT47^2Arc(8) 1901 428911364 Power N-CT47^2Arc(7) 1942 431903680 Power N-CT47^2Arc(6) 1984 434895996 Power N-CT47^2Arc(5) 2027 437888312 Power N-CT47^2Arc(4) 2071 440880628 Power N-CT47^2Arc(3) 2116 443872944 Power N-CT47^2T1T1 2162 446865260 Power N-CT47^2T1 2210 449857576 Power N-CT47^2+1 2211 469022176 Add 1 factors 2212 476212276 Add 2 factors 2213 485869456 Add 3 factors 2214 488897236 Add 4 factors 2215 489736185 Add 5 factors 2221 490507746 Add 11 factors 2222 509672346 Add 11 factors 2223 516045412 Add 13 factors 2224 526519626 Add 11 factors 2225 529547406 Add 11 factors 2226 530386355 Add 11 factors 2232 531157916 Add 11 factors 2352 534718778 Power CT31^3T19T17T17 2366 534854138 Power CT31^3T18T18T17 2592 535437032 Power CT31^3T19T19T13 2880 535753298 Power CT31^3T19T19T11 3168 536235298 Power CT31^3T19T19T9 3456 536330406 Power CT31^3T19T19T7 3744 537629466 Power CT31^3T19T18T7 4032 538793166 Power CT31^3T19T17T7 4056 538928526 Power CT31^3T18T18T7 4368 540092226 Power CT31^3T18T17T7 4704 541255926 Power CT31^3T17T17T7 4800 541713338 Power CT31^3T19T11T11 5184 541974180 Power CT31^3T19T13T7 5280 542195338 Power CT31^3T19T11T9 5760 542290446 Power CT31^3T19T11T7 5808 542677338 Power CT31^3T19T9T9 6336 542772446 Power CT31^3T19T9T7 6912 542867554 Power CT31^3T19T7T7 7488 544166614 Power CT31^3T18T7T7 8064 545330314 Power CT31^3T17T7T7 8640 546647194 Power CT31^3T16T7T7 9216 548126104 Power CT31^3T15T7T7 9600 548250486 Power CT31^3T11T11T7 10000 548511328 Power CT31^3T13T7T7

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