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

Last Updated Tue Jan 31 05:20:10 MST 2012

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 30 579983846 Martirosyan-Tran van Trung 32 591232667 Martirosyan-Tran van Trung 34 606834576 Martirosyan-Tran van Trung 36 619797850 Martirosyan-Tran van Trung 38 630442175 Martirosyan-Tran van Trung 40 637563591 Martirosyan-Tran van Trung 42 697327370 Martirosyan-Tran van Trung 44 698463232 Martirosyan-Tran van Trung 46 699335487 Martirosyan-Tran van Trung 48 701664792 Martirosyan-Tran van Trung 49 945499772 Add a factor 50 1061295021 Martirosyan-Tran van Trung 52 1065201171 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 CT16^2T6S15 80 1603375185 Power CT16^2Tlev 82 1605917170 Power CT16^2T5S15 88 1610270367 Power CT16^2T4S15 96 1611128179 Power CT16^2TD(4):4,4,4,4,4 112 1616469422 Power CT16^2Arc(18):9 twos,0 ones 120 1624753520 Power CT16^2Arc(16) 121 1630098104 Power CT16^2Arc(15) 123 1635442688 Power CT16^2Arc(14) 126 1640787272 Power CT16^2Arc(13) 130 1646131856 Power CT16^2Arc(12) 135 1651476440 Power CT16^2Arc(11) 141 1656821024 Power CT16^2Arc(10) 148 1662165608 Power CT16^2Arc(9) 156 1667510192 Power CT16^2Arc(8) 165 1672854776 Power CT16^2Arc(7) 175 1678199360 Power CT16^2Arc(6) 186 1683543944 Power CT16^2Arc(5) 198 1688888528 Power CT16^2Arc(4) 211 1694233112 Power CT16^2Arc(3) 225 1699577696 Power CT16^2T1T1 240 1704922280 Power CT16^2T1 256 1710266864 Power CT16^2 272 1794655019 Power CT17^2T1 289 1800280896 Power CT17^2 290 1895032512 Power CT17^2+1 291 1969836420 Power CT19^2Arc(4) 307 1976070079 Power CT19^2Arc(3) 324 1982303738 Power CT19^2T1T1 342 1988537397 Power CT19^2T1 361 1994771056 Power CT19^2 362 2099758992 Power CT19^2+1 368 2327429909 Power CT23^2T7 380 2328410476 Power CT23^2T4T3 391 2333055786 Power CT23^2T6 400 2334972222 Power CT23^2T3T3 414 2338977762 Power CT23^2T5 437 2345211421 Power CT23^2T4 460 2351773167 Power CT23^2T3 529 2368573873 perfect hash family16,529,23,c fuse fuse fuse 530 2368574112 Power CT23^2+1 531 2882921212 Add a factor 532 3469244872 Add a factor 553 3617935628 Power CT25^2Arc(3) 576 3714040360 Power CT25^2T1T1 600 3810145092 Power CT25^2T1 625 3906249615 perfect hash family16,625,25,c fuse fuse fuse fuse fuse 626 3906249824 Power CT25^2+1 627 4630383524 Add a factor 628 5374669384 Add a factor 651 5768888004 Power CT27^2Arc(3) 676 5912167864 Power CT27^2T1T1 702 6055447724 Power CT27^2T1 730 6198727584 Power CT27^2+1 731 6987712464 Add a factor 736 7111889843 Martirosyan-Tran van Trung 760 7118498150 Martirosyan-Tran van Trung 768 7135471800 Martirosyan-Tran van Trung 782 7138166756 Martirosyan-Tran van Trung 800 7146008910 Martirosyan-Tran van Trung 816 7215956302 Martirosyan-Tran van Trung 828 7221346222 Martirosyan-Tran van Trung 874 7242849801 Martirosyan-Tran van Trung 912 7262193211 Martirosyan-Tran van Trung 920 7267607379 Martirosyan-Tran van Trung 960 7312779633 Martirosyan-Tran van Trung 966 7393505807 Martirosyan-Tran van Trung 1008 7395201137 Martirosyan-Tran van Trung 1012 7397908225 Martirosyan-Tran van Trung 1058 7398827878 Martirosyan-Tran van Trung 1060 7759102820 Martirosyan-Tran van Trung 1062 8528352020 Martirosyan-Tran van Trung 1076 8908124519 Power N-CT41^2T5S13 1134 8918768844 Power N-CT41^2T3S13 1198 8925890260 Power N-CT41^2Arc(14) 1226 8985654039 Power N-CT41^2Arc(13) 1255 9045417818 Power N-CT41^2Arc(12) 1285 9105181597 Power N-CT41^2Arc(11) 1316 9164945376 Power N-CT41^2Arc(10) 1348 9224709155 Power N-CT41^2Arc(9) 1381 9284472934 Power N-CT41^2Arc(8) 1415 9344236713 Power N-CT41^2Arc(7) 1450 9404000492 Power N-CT41^2Arc(6) 1486 9463764271 Power N-CT41^2Arc(5) 1523 9523528050 Power N-CT41^2Arc(4) 1561 9583291829 Power N-CT41^2Arc(3) 1600 9643055608 Power N-CT41^2T1T1 1640 9702819387 Power N-CT41^2T1 1641 9715313869 Power N-CT43^2Arc(2)T3 1680 9716449731 Power N-CT43^2T3T1 1720 9717585593 Power N-CT43^2T3 1748 9749755152 Power N-CT47^2T9T1 1786 9752084457 Power N-CT47^2T9 1801 9754547263 Power N-CT47^2Arc(2)T7 1840 9756876568 Power N-CT47^2T7T1 1880 9759205873 Power N-CT47^2T7 1901 9807001939 Power N-CT47^2Arc(7) 1942 9809331244 Power N-CT47^2Arc(6) 1984 9811660549 Power N-CT47^2Arc(5) 2027 9813989854 Power N-CT47^2Arc(4) 2071 9816319159 Power N-CT47^2Arc(3) 2116 9818648464 Power N-CT47^2T1T1 2162 9820977769 Power N-CT47^2T1 2210 9823307074 Power N-CT47^2+1 2211 10931664854 Add a factor 2212 12040022634 Add a factor 2213 13148380414 Add a factor 2214 14256738194 Add a factor 2257 14396491396 Power CT49^2Arc(3) 2304 14640326376 Power CT49^2T1T1 2352 14884161356 Power CT49^2T1 2401 15127996336 Power CT49^2 2402 16240982896 Add a factor 2413 16750039960 Power N-CT53^2Arc(8) 2548 16839100384 Power CT31^3T18T17T17 2744 16843923871 Power CT31^3T17T17T17 2940 16849001225 Power CT31^3T17T17T16 3150 16854078579 Power CT31^3T17T16T16 3375 16859155933 Power CT31^3T16T16T16 3600 16864500517 Power CT31^3T16T16T15 3840 16869845101 Power CT31^3T16T15T15 4096 16875189685 Power CT31^3T15T15T15 4352 16880815562 Power CT31^3T15T15T14 4624 16886441439 Power CT31^3T15T14T14 4913 16892067316 Power CT31^3T14T14T14 5202 16897989292 Power CT31^3T14T14T13 5508 16903911268 Power CT31^3T14T13T13 5832 16909833244 Power CT31^3T13T13T13 6156 16916066903 Power CT31^3T13T13T12 6528 16921959765 Power CT31^3T15T14T7 6936 16927585642 Power CT31^3T14T14T7 7344 16933507618 Power CT31^3T14T13T7 7776 16939429594 Power CT31^3T13T13T7 8208 16945663253 Power CT31^3T13T12T7 8664 16951896912 Power CT31^3T12T12T7 9216 16957478091 Power CT31^3T15T7T7 9792 16963103968 Power CT31^3T14T7T7 10000 16969025944 Power CT31^3T13T7T7

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