Table for CAN(6,k,20) for k up to 10000

Last Updated Sun Nov 22 06:45:17 MST 2009

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,20) 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 64000000 composition 8 70914127 Add a symbol 9 74646449 Add a symbol 10 78575209 Add a symbol 11 82710746 Add a symbol 12 87063943 Add a symbol 13 91646255 Add a symbol 14 96469742 Add a symbol 15 101547096 Add a symbol 16 106891680 Add a symbol 17 112517557 Add a symbol 18 118439533 Add a symbol 19 124673192 Add a symbol 20 131234938 Add a symbol 24 148035883 orthogonal array fuse fuse fuse 26 244140615 orthogonal array fuse fuse fuse fuse fuse 28 387420475 orthogonal array fuse fuse fuse fuse fuse fuse fuse 29 589362735 Add a factor 31 592143481 perfect hash family4,31,23,c fuse fuse fuse 32 646849011 Martirosyan-Tran van Trung 34 658100750 Martirosyan-Tran van Trung 36 669944684 Martirosyan-Tran van Trung 38 680029339 Martirosyan-Tran van Trung 40 686591085 Martirosyan-Tran van Trung 48 703392030 Martirosyan-Tran van Trung 49 947227010 Add a factor 50 1075696810 Martirosyan-Tran van Trung 52 1078040500 Martirosyan-Tran van Trung 53 1371405101 perfect hash family11,53,19 54 1421274384 perfect hash family12,54,18 55 1430460815 perfect hash family11,60,20S2 57 1437022561 perfect hash family11,60,20T1 60 1443584307 perfect hash family11,60,20 65 1466340064 perfect hash family16,65,13 66 1543515856 perfect hash family16,66,14 67 1587341433 perfect hash family15,80,16S3 71 1592686017 perfect hash family15,80,16S2 75 1598030601 perfect hash family15,80,16T1 76 1601781633 Power 16^2T6S15 80 1603375185 Power 16^2Tlev 82 1605917170 Power 16^2T5S15 88 1610270367 Power 16^2T4S15 94 1614852679 Power 16^2T3S15 100 1619676166 Power 16^2T2S15 106 1624753520 Power 16^2S16 111 1630098104 Power 16^2S15 117 1635442688 Power 16^2S14 122 1640787272 Power 16^2S13 127 1646131856 Power 16^2S12 133 1651476440 Power 16^2S11 140 1656821024 Power 16^2S10 148 1662165608 Power 16^2S9 156 1667510192 Power 16^2S8 165 1672854776 Power 16^2S7 175 1678199360 Power 16^2S6 186 1683543944 Power 16^2S5 198 1688888528 Power 16^2S4 211 1694233112 Power 16^2S3 225 1699577696 Power 16^2T1T1 240 1704922280 Power 16^2T1 256 1710266864 Power 16^2 272 1794655019 Power 17^2T1 289 1800280896 Power 17^2 290 1895032512 Power 17^2+1 291 1969836420 Power 19^2S4 307 1976070079 Power 19^2S3 324 1982303738 Power 19^2T1T1 342 1988537397 Power 19^2T1 361 1994771056 Power 19^2 362 2099758992 Power 19^2+1 368 2327429909 Power 23^2T7 380 2328410476 Power 23^2T4T3 391 2333055786 Power 23^2T6 400 2334972222 Power 23^2T3T3 414 2338977762 Power 23^2T5 437 2345211421 Power 23^2T4 460 2351773167 Power 23^2T3 529 2368573873 perfect hash family16,529,23,c fuse fuse fuse 530 2368574112 Power 23^2+1 531 2886398972 Add a factor 532 3413068712 Add a factor 553 3617935628 Power 25^2S3 576 3714040360 Power 25^2T1T1 600 3810145092 Power 25^2T1 625 3906249615 perfect hash family16,625,25,c fuse fuse fuse fuse fuse 626 3906249824 Power 25^2+1 627 4608981164 Add a factor 628 5311712504 Add a factor 651 5768888004 Power 27^2S3 676 5912167864 Power 27^2T1T1 702 6055447724 Power 27^2T1 730 6198727584 Power 27^2+1 731 6991145764 Add a factor 735 7253757451 perfect hash family49,735,23,c fuse fuse fuse 736 7552426793 Martirosyan-Tran van Trung 760 7559033222 Martirosyan-Tran van Trung 782 7563678532 Martirosyan-Tran van Trung 800 7571516926 Martirosyan-Tran van Trung 828 7575522466 Martirosyan-Tran van Trung 874 7585607121 Martirosyan-Tran van Trung 920 7592168867 Martirosyan-Tran van Trung 1058 7608969573 Martirosyan-Tran van Trung 1060 7656266644 Martirosyan-Tran van Trung 1062 8429202984 Martirosyan-Tran van Trung 1064 9210984204 Martirosyan-Tran van Trung 1128 9292132259 Power N47^2T23 1222 9388236991 Power N47^2T21 1316 9531516851 Power N47^2T19 1348 9696279901 Power N41^2S9 1381 9713080846 Power N41^2S8 1415 9729881791 Power N41^2S7 1457 9736239857 Power N47^2T16 1486 9763483681 Power N41^2S5 1523 9780284626 Power N41^2S4 1561 9797085571 Power N41^2S3 1598 9802197126 Power N47^2T13 1600 9813886516 Power N41^2T1T1 1692 9814041060 Power N47^2T11 1786 9824125715 Power N47^2T9 1880 9830687461 Power N47^2T7 2210 9847488406 Power N47^2+1 2211 11045120726 Add a factor 2212 12242753046 Add a factor 2213 13440385366 Add a factor 2257 14424127204 Power 49^2S3 2304 14667962184 Power 49^2T1T1 2352 14911797164 Power 49^2T1 2401 15155632144 Power 49^2 2402 16353264464 Add a factor 2413 16852754592 Power N53^2S8 2459 17146119193 Power N53^2S7 2511 17321453816 Power 31^3T22T22 2604 17323224861 Power 31^3T24T19 2790 17325382576 Power 31^3T22T21 2821 17327807173 Power 31^3T24T18 3100 17329311336 Power 31^3T21T21 3410 17333446873 Power 31^3T21T20 3751 17337582410 Power 31^3T20T20 4092 17341935607 Power 31^3T20T19 4464 17346288804 Power 31^3T19T19 4836 17350871116 Power 31^3T19T18 5239 17355453428 Power 31^3T18T18 5642 17360276915 Power 31^3T18T17 6076 17365100402 Power 31^3T17T17 6510 17370177756 Power 31^3T17T16 6975 17375255110 Power 31^3T16T16 7440 17380599694 Power 31^3T16T15 7936 17385944278 Power 31^3T15T15 8432 17391570155 Power 31^3T15T14 8959 17397196032 Power 31^3T14T14 9486 17403118008 Power 31^3T14T13 10000 17409039984 Power 31^3T13T13

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