Table for CAN(5,k,20) for k up to 10000

Last Updated Fri Sep 20 11:41:02 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;5,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 6 3200000 Derive from strength 6 7 3545706 Derive from strength 6 8 3732322 Derive from strength 6 9 3928760 Derive from strength 6 10 4135536 Add a symbol 11 4353195 Add a symbol 12 4582310 Add a symbol 13 4823484 Add a symbol 14 5077351 Add a symbol 15 5344580 Add a symbol 16 5625873 Add a symbol 17 5921971 Add a symbol 18 6233653 Add a symbol 24 6436337 orthogonal array fuse fuse fuse 26 9765615 orthogonal array fuse fuse fuse fuse fuse 28 14348893 orthogonal array fuse fuse fuse fuse fuse fuse fuse 31 19308977 perfect hash family3,31,23,c fuse fuse fuse 32 19309008 perfect hash family3,32,24 34 20583796 Martirosyan-Tran van Trung 36 20915618 Martirosyan-Tran van Trung 38 21118302 Martirosyan-Tran van Trung 40 21319702 Martirosyan-Tran van Trung 42 23889106 Martirosyan-Tran van Trung 44 23937426 Martirosyan-Tran van Trung 46 23974666 Martirosyan-Tran van Trung 48 24074434 Martirosyan-Tran van Trung 49 32345134 AZ1 50 32771556 Martirosyan-Tran van Trung 52 32923746 Martirosyan-Tran van Trung 53 42168006 AZ1 54 43534166 Martirosyan-Tran van Trung 56 44851668 perfect hash family7,62,21T3 64 45054257 perfect hash family7,64,23,c fuse fuse fuse 65 45054352 perfect hash family7,65,24 70 46579180 Power CT11^2Arc(6) 76 46796839 Power CT11^2Arc(5) 83 47014498 Power CT11^2Arc(4) 91 47232157 Power CT11^2Arc(3) 100 47449816 Power CT11^2T1T1 110 47667475 Power CT11^2T1 121 47885134 Power CT11^2 122 50405399 Power CT11^2+1 123 52093617 Power CT13^2Arc(4) 133 52334791 Power CT13^2Arc(3) 144 52575965 Power CT13^2T1T1 156 52817139 Power CT13^2T1 169 53058313 Power CT13^2 170 55850850 Power CT13^2+1 171 58790369 Power CT13^2+2 175 60196834 Power CT16^2Arc(6) 186 60478127 Power CT16^2Arc(5) 198 60759420 Power CT16^2Arc(4) 211 61040713 Power CT16^2Arc(3) 225 61322006 Power CT16^2T1T1 240 61603299 Power CT16^2T1 256 61884592 Power CT16^2 276 62509333 Power N-CT23^2T11 299 62750507 Power N-CT23^2T10 322 63004374 Power N-CT23^2T9 345 63271603 Power N-CT23^2T8 368 63552896 Power N-CT23^2T7 391 63848994 Power N-CT23^2T6 414 64160676 Power N-CT23^2T5 530 64363360 Power N-CT23^2+1 531 73607620 AZ1 532 80797220 Add 2 factors 533 83837220 Add 3 factors 534 93081480 Add 3 factors 553 97433920 Power CT25^2Arc(3) 576 100763198 Power CT25^2T1T1 600 104092476 Power CT25^2T1 625 107421615 perfect hash family11,625,25,c fuse fuse fuse fuse fuse 626 107421754 Power CT25^2+1 627 119292574 AZ1 628 126565774 Add 2 factors 648 127443887 Power CT23^3T15T14T14 660 127542776 Power CT23^3T17T13T12 729 127640325 Power CT23^3T14T14T14 810 127847101 Power CT23^3T14T14T13 900 128053877 Power CT23^3T14T13T13 1000 128260653 Power CT23^3T13T13T13 1100 128478312 Power CT23^3T13T13T12 1210 128695971 Power CT23^3T13T12T12 2116 128726720 Power CT23^3Tlev 2197 130324497 Power CT23^3T10T10T10 2300 130561454 Power CT23^3T13T13 2366 130578364 Power CT23^3T10T10T9 2530 130779113 Power CT23^3T13T12 2548 130832231 Power CT23^3T10T9T9 2783 130996772 Power CT23^3T12T12 3036 131225887 Power CT23^3T12T11 3312 131455002 Power CT23^3T11T11 3588 131696176 Power CT23^3T11T10 3887 131937350 Power CT23^3T10T10 4186 132191217 Power CT23^3T10T9 4508 132445084 Power CT23^3T9T9 4761 132655479 Power CT23^3T14 4830 132712313 Power CT23^3T9T8 5290 132862255 Power CT23^3T13 5819 133079914 Power CT23^3T12 6348 133309029 Power CT23^3T11 6877 133550203 Power CT23^3T10 7406 133804070 Power CT23^3T9 7935 134071299 Power CT23^3T8 8464 134352592 Power CT23^3T7 8993 134648690 Power CT23^3T6 9522 134960372 Power CT23^3T5 10000 135162737 perfect hash family21,12167,23,c fuse fuse fuse

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