Table for CAN(6,k,20) 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,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 555774852 Martirosyan-Tran van Trung 32 569405537 Martirosyan-Tran van Trung 34 586126786 Martirosyan-Tran van Trung 36 598530390 Martirosyan-Tran van Trung 38 608615045 Martirosyan-Tran van Trung 40 620773491 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 955998032 Add 1 factors 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 1 factors 532 3067806412 Add 2 factors 533 3211598412 Add 3 factors 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 4599992264 Add 1 factors 628 4837408664 Add 2 factors 629 4982872664 Add 3 factors 630 5533684850 Add 5 factors 648 5617720739 Add 23 factors 649 5714475738 Add 23 factors 651 5768888004 Power CT27^2Arc(3) 676 5912167864 Power CT27^2T1T1 702 6055447724 Power CT27^2T1 720 6119967163 Martirosyan-Tran van Trung 722 6126800399 Martirosyan-Tran van Trung 730 6198727584 Power CT27^2+1 736 6459459252 Martirosyan-Tran van Trung 760 6466065681 Martirosyan-Tran van Trung 768 6488996601 Martirosyan-Tran van Trung 770 6505907373 Martirosyan-Tran van Trung 782 6508532559 Martirosyan-Tran van Trung 800 6516372759 Martirosyan-Tran van Trung 816 6520378299 Martirosyan-Tran van Trung 828 6523003487 Martirosyan-Tran van Trung 874 6533088142 Martirosyan-Tran van Trung 912 6547263376 Martirosyan-Tran van Trung 920 6615754136 Martirosyan-Tran van Trung 950 6640345192 Martirosyan-Tran van Trung 960 6658939194 Martirosyan-Tran van Trung 966 6736062740 Martirosyan-Tran van Trung 968 6736064626 Martirosyan-Tran van Trung 978 6738771714 Martirosyan-Tran van Trung 1008 6741478802 Martirosyan-Tran van Trung 1012 6744185890 Martirosyan-Tran van Trung 1058 6744187782 Martirosyan-Tran van Trung 1060 6806362925 Martirosyan-Tran van Trung 1062 7496350965 Martirosyan-Tran van Trung 1064 7817838565 Martirosyan-Tran van Trung 1066 8019390565 Martirosyan-Tran van Trung 1068 8601368721 Martirosyan-Tran van Trung 1076 8668585759 Power N-CT41^2T5S13 1134 8678670414 Power N-CT41^2T3S13 1198 8690828860 Power N-CT41^2Arc(14) 1226 8767382739 Power N-CT41^2Arc(13) 1255 8843936618 Power N-CT41^2Arc(12) 1285 8920490497 Power N-CT41^2Arc(11) 1316 8997044376 Power N-CT41^2Arc(10) 1348 9073598255 Power N-CT41^2Arc(9) 1370 9129225660 Power N-CT37^2+1 1381 9150152134 Power N-CT41^2Arc(8) 1415 9226706013 Power N-CT41^2Arc(7) 1450 9303259892 Power N-CT41^2Arc(6) 1486 9379813771 Power N-CT41^2Arc(5) 1523 9456367650 Power N-CT41^2Arc(4) 1561 9532921529 Power N-CT41^2Arc(3) 1600 9609475408 Power N-CT41^2T1T1 1640 9686029287 Power N-CT41^2T1 1641 9698523769 Power N-CT43^2Arc(2)T3 1680 9699659631 Power N-CT43^2T3T1 1720 9700795493 Power N-CT43^2T3 1748 9727928022 Power N-CT47^2T9T1 1786 9730257327 Power N-CT47^2T9 1801 9737757163 Power N-CT47^2Arc(2)T7 1840 9740086468 Power N-CT47^2T7T1 1880 9742415773 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 10788957374 Add 1 factors 2212 11144789374 Add 2 factors 2213 11338285374 Add 3 factors 2214 12117916886 Add 4 factors 2215 12175480543 Add 5 factors 2233 12259516432 Add 23 factors 2235 12949568074 Add 25 factors 2236 13774494732 Add 23 factors 2237 14271050374 Add 25 factors 2238 14464546374 Add 25 factors 2257 14532968776 Power CT49^2Arc(3) 2304 14787302016 Power CT49^2T1T1 2352 15041635256 Power CT49^2T1 2401 15295968496 Power CT49^2 2548 16227940744 Power CT31^3T18T17T17 2744 16232764231 Power CT31^3T17T17T17 2940 16237841585 Power CT31^3T17T17T16 3150 16242918939 Power CT31^3T17T16T16 3375 16247996293 Power CT31^3T16T16T16 3600 16253340877 Power CT31^3T16T16T15 3840 16258685461 Power CT31^3T16T15T15 4096 16264030045 Power CT31^3T15T15T15 4352 16269655922 Power CT31^3T15T15T14 4624 16275281799 Power CT31^3T15T14T14 4913 16280907676 Power CT31^3T14T14T14 5202 16286829652 Power CT31^3T14T14T13 5508 16292751628 Power CT31^3T14T13T13 5832 16298673604 Power CT31^3T13T13T13 6156 16304907263 Power CT31^3T13T13T12 6528 16310800125 Power CT31^3T15T14T7 6936 16316426002 Power CT31^3T14T14T7 7344 16322347978 Power CT31^3T14T13T7 7776 16328269954 Power CT31^3T13T13T7 8208 16334503613 Power CT31^3T13T12T7 8664 16340737272 Power CT31^3T12T12T7 9216 16346318451 Power CT31^3T15T7T7 9792 16351944328 Power CT31^3T14T7T7 10000 16357866304 Power CT31^3T13T7T7

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