Table for CAN(5,k,10) 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,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 6 100000 Derive from strength 6 7 120000 Ji-Li-Yin 8 137173 Add a symbol 9 149043 orthogonal array fuse postop NCK 10 155522 orthogonal array fuse postop NCK 11 158738 orthogonal array fuse postop NCK 12 159960 orthogonal array fuse postop NCK 13 276330 AZ1 14 346809 orthogonal array fuse fuse fuse postop NCK 15 476211 perfect hash family3,15,11 16 479877 perfect hash family3,16,12 18 554727 Martirosyan-Tran van Trung 20 566642 Martirosyan-Tran van Trung 22 588620 Martirosyan-Tran van Trung 24 595218 Martirosyan-Tran van Trung 25 806718 AZ1 26 934059 Martirosyan-Tran van Trung 28 1042422 Martirosyan-Tran van Trung 29 1262027 Add 11 factors 30 1275152 Add 11 factors 32 1279672 perfect hash family8,32,12 33 1321220 Add 11 factors 34 1332658 Add 11 factors 35 1340138 Add 11 factors 37 1439631 perfect hash family9,37,12 38 1522919 Martirosyan-Tran van Trung 40 1524197 Martirosyan-Tran van Trung 44 1587370 Power CT11^2Tlev 45 1599590 perfect hash family10,45,12 46 1660818 Martirosyan-Tran van Trung 48 1665804 Power CT11^2T5T3 49 1668631 Power CT11^2T4T4 50 1674458 Power CT11^2Trin1,2,5 54 1677674 Power CT11^2T5T2 55 1680937 Power CT11^2Arc(2)T5 60 1684153 Power CT11^2T5T1 66 1687369 Power CT11^2T5 70 1704153 Power CT11^2T4T1 77 1707369 Power CT11^2T4 80 1721326 Power CT11^2T3T1 88 1724542 Power CT11^2T3 90 1733196 Power CT11^2T2T1 99 1736412 Power CT11^2T2 100 1739675 Power CT11^2T1T1 110 1742891 Power CT11^2T1 121 1746107 Power CT11^2 122 1759549 Power CT11^2+1 123 1998859 AZ1 124 2193259 Add 2 factors 125 2400099 Add 3 factors 126 2531859 Add 4 factors 132 2579467 Add 11 factors 133 2592909 Add 11 factors 144 2806879 Power CT13^2T1T1 156 2923249 Power CT13^2T1 169 3039619 Power CT13^2 176 3365951 Martirosyan-Colbourn 180 3378339 Martirosyan-Colbourn 192 3381555 Martirosyan-Colbourn 198 3387081 Martirosyan-Colbourn 200 3390344 Martirosyan-Colbourn 204 3393560 Martirosyan-Colbourn 216 3511949 Martirosyan-Tran van Trung 220 3513380 Martirosyan-Tran van Trung 242 3516596 Martirosyan-Tran van Trung 244 3552762 Martirosyan-Tran van Trung 246 3792072 Martirosyan-Tran van Trung 248 3986472 Martirosyan-Tran van Trung 250 4193312 Martirosyan-Tran van Trung 252 4325072 Martirosyan-Tran van Trung 264 4372680 Martirosyan-Tran van Trung 266 4396877 Martirosyan-Tran van Trung 267 4790717 AZ1 268 5027997 Martirosyan-Tran van Trung 269 5294057 Add 3 factors 270 5321783 Martirosyan-Tran van Trung 288 5369015 Martirosyan-Tran van Trung 304 5579645 Power N-CT19^2T3 307 5630665 Power N-CT19^2Arc(3) 324 5642580 Power N-CT19^2T1T1 342 5654495 Power N-CT19^2T1 362 5666410 Power N-CT19^2+1 368 5836829 Power N-CT23^2T7 383 5888420 Power N-CT23^2Trin1,3,3 400 5895018 Power N-CT23^2T3T3 403 5903800 Power N-CT23^2Arc(3)T3 421 5910398 Power N-CT23^2Arc(2)T3 440 5916996 Power N-CT23^2T3T1 460 5923594 Power N-CT23^2T3 463 5932376 Power N-CT23^2Arc(3) 484 5938974 Power N-CT23^2T1T1 506 5945572 Power N-CT23^2T1 530 5952170 Power N-CT23^2+1 531 6439070 AZ1 532 6709070 Add 2 factors 533 6996970 Add 3 factors 534 7128730 Add 4 factors 541 7189780 Add 11 factors 542 7676680 Add 11 factors 543 7946680 Add 11 factors 544 8234580 Add 11 factors 553 8239387 Power CT25^2Arc(3) 576 8450887 Power CT25^2T1T1 600 8662387 Power CT25^2T1 606 8822834 Martirosyan-Colbourn 612 8823716 Martirosyan-Colbourn 614 8823734 Martirosyan-Colbourn 618 8835649 Martirosyan-Colbourn 624 8839267 Martirosyan-Colbourn 642 8839303 Martirosyan-Colbourn 648 8846755 Martirosyan-Colbourn 684 8860173 Martirosyan-Colbourn 690 8872088 Martirosyan-Colbourn 714 8875958 Martirosyan-Colbourn 720 8878073 Martirosyan-Colbourn 724 8883914 Martirosyan-Colbourn 726 9103694 Martirosyan-Colbourn 728 9112559 Martirosyan-Colbourn 766 9114789 Martirosyan-Colbourn 792 9121387 Martirosyan-Colbourn 800 9145579 Martirosyan-Colbourn 806 9154361 Martirosyan-Colbourn 842 9160959 Martirosyan-Colbourn 864 9167557 Martirosyan-Colbourn 880 9220171 Martirosyan-Colbourn 920 9230504 Martirosyan-Colbourn 926 9239286 Martirosyan-Colbourn 960 9245884 Martirosyan-Colbourn 968 9251410 Martirosyan-Colbourn 1012 9258008 Martirosyan-Colbourn 1030 9264606 Martirosyan-Colbourn 1040 9265506 Martirosyan-Colbourn 1050 9265524 Martirosyan-Colbourn 1060 9272094 Martirosyan-Colbourn 1062 9758994 Martirosyan-Colbourn 1064 10028994 Martirosyan-Colbourn 1066 10316894 Martirosyan-Colbourn 1068 10448654 Martirosyan-Colbourn 1070 10509704 Martirosyan-Colbourn 1080 10510604 Martirosyan-Colbourn 1082 10512089 Martirosyan-Colbourn 1110 10552856 perfect hash family66,1332,12T2 1120 10554850 perfect hash family66,1332,12S2 1221 10556072 perfect hash family66,1332,12T1 1332 10557294 perfect hash family66,1332,12 1333 11110974 AZ1 1440 11189345 Power CT23^3T13T11T11 1452 11191339 Power CT23^3T12T12T11 1584 11192561 Power CT23^3T12T11T11 1728 11193783 Power CT23^3T11T11T11 1872 11310153 Power CT23^3T11T11T10 2016 11380632 Power CT23^3T11T11T9 2028 11426523 Power CT23^3T11T10T10 2184 11497002 Power CT23^3T11T10T9 2304 11513700 Power CT23^3T11T11T7 2352 11567481 Power CT23^3T11T9T9 2376 11587328 Power CT23^3T12T11T5 2592 11588550 Power CT23^3T11T11T5 2640 11599243 Power CT23^3T12T11T3 2880 11600465 Power CT23^3T11T11T3 2904 11621221 Power CT23^3T12T11T1 3168 11622443 Power CT23^3T11T11T1 3312 11629041 Power CT23^3T11T11 3432 11738813 Power CT23^3T11T10T1 3588 11745411 Power CT23^3T11T10 3696 11809292 Power CT23^3T11T9T1 3864 11815890 Power CT23^3T11T9 3887 11861781 Power CT23^3T10T10 4004 11925662 Power CT23^3T10T9T1 4186 11932260 Power CT23^3T10T9 4224 11942360 Power CT23^3T11T7T1 4416 11948958 Power CT23^3T11T7 4508 12002739 Power CT23^3T9T9 4800 12007147 Power CT23^3T11T3T3 4968 12023808 Power CT23^3T11T5 5280 12029125 Power CT23^3T11T3T1 5520 12035723 Power CT23^3T11T3 5556 12044505 Power CT23^3T11S3 5808 12051103 Power CT23^3T11T1T1 6072 12057701 Power CT23^3T11T1 6348 12064299 Power CT23^3T11 6578 12174071 Power CT23^3T10T1 6877 12180669 Power CT23^3T10 7084 12244550 Power CT23^3T9T1 7406 12251148 Power CT23^3T9 7408 12364422 Power CT23^3T7S3 7744 12371020 Power CT23^3T7T1T1 8096 12377618 Power CT23^3T7T1 8464 12384216 Power CT23^3T7 8800 12435807 Power CT23^3T3T3T1 9200 12442405 Power CT23^3T3T3 9260 12451187 Power CT23^3T3S3 9680 12457785 Power CT23^3T3T1T1 10000 12464383 Power CT23^3T3T1

Graph: