Table for CAN(5,k,6) for k up to 10000

Last Updated Tue Mar 8 20:11:31 MST 2022

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,6) 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 7776 Derive from strength 6

7 10368 Ji-Li-Yin

8 11664 Xu-Ji-Dong

9 18475 Torres-Jimenez

10 21985 Density Cyclic (Colbourn) postop NCK

11 24602 Density Cyclic (Colbourn) postop NCK

12 27131 Density Cyclic (Colbourn) postop NCK

13 29279 Density Cyclic (Colbourn) postop NCK

14 31460 Density Cyclic (Colbourn) postop NCK

15 33505 Density Cyclic (Colbourn) postop NCK

16 35382 Density Cyclic (Colbourn) postop NCK

17 37184 Density Cyclic (Colbourn) postop NCK

18 38867 Density Cyclic (Colbourn) postop NCK

19 40536 Density Cyclic (Colbourn) postop NCK

20 42044 Density Cyclic (Colbourn) postop NCK

21 43531 Density Cyclic (Colbourn) postop NCK

22 45018 Density Cyclic (Colbourn)

23 46362 Density Cyclic (Colbourn)

24 47634 Density Cyclic (Colbourn)

25 48906 Density Cyclic (Colbourn)

26 52814 IPOGF postop MPO (TJ-RC)

27 54032 IPOGF postop MPO (TJ-RC)

28 55275 IPOGF postop MPO (TJ-RC)

29 56353 IPOGF postop MPO (TJ-RC)

30 57503 IPOGF postop MPO (TJ-RC)

31 58576 IPOGF postop MPO (TJ-RC)

32 59612 IPOGF postop MPO (TJ-RC)

33 60608 IPOGF postop MPO (TJ-RC)

34 61612 IPOGF postop MPO (TJ-RC)

35 62557 IPOGF postop MPO (TJ-RC)

36 63519 IPOGF postop MPO (TJ-RC)

37 64385 IPOGF postop MPO (TJ-RC)

38 65251 IPOGF postop MPO (TJ-RC)

39 66124 IPOGF postop MPO (TJ-RC)

40 66953 IPOGF postop MPO (TJ-RC)

41 67865 IPOGF postop MPO (TJ-RC)

42 68609 IPOGF postop MPO (TJ-RC)

43 69407 IPOGF postop MPO (TJ-RC)

44 70177 IPOGF postop MPO (TJ-RC)

45 71062 IPOGF postop MPO (TJ-RC)

46 71778 IPOGF postop MPO (TJ-RC)

47 83627 3,2-restricted SCPHF RE (CL) fuse

52 84029 CPHF IPO 5 (WCS) fuse

54 95681 SCPHF CLS - other fuse

59 96017 4,4-Restricted SCPHF RE (CL) fuse

61 98411 4-Restricted SCPHF RE (CL) fuse

67 100469 3-Restricted SCPHF RE (CL) fuse

68 100763 2-Restricted SCPHF RE (CL) fuse

69 100805 SCPHF Random Extension (CLS) fuse

78 100835 CPHF IPO 6 (WCS) fuse

82 112817 4,4-Restricted SCPHF RE (CL) fuse

93 115211 4-Restricted SCPHF RE (CL) fuse

96 117269 3-Restricted SCPHF RE (CL) fuse

99 117563 2-Restricted SCPHF RE (CL) fuse

101 117605 SCPHF Random Extension (CLS) fuse

118 117641 CPHF IPO 7 (WCS) fuse

121 129617 4,4-Restricted SCPHF RE (CL) fuse

132 132011 4-Restricted SCPHF RE (CL) fuse

140 134069 3-Restricted SCPHF RE (CL) fuse

148 134363 2-Restricted SCPHF RE (CL) fuse

149 134405 SCPHF Random Extension (CLS) fuse

188 134447 CPHF IPO 8 (WCS) fuse

195 148811 4-Restricted SCPHF RE (CL) fuse

201 150869 3-Restricted SCPHF RE (CL) fuse

205 151163 2-Restricted SCPHF RE (CL) fuse

209 151205 SCPHF Random Extension (CLS) fuse

277 151253 CPHF IPO 9 (WCS) fuse

284 165611 4-Restricted SCPHF RE (CL) fuse

315 167669 3-Restricted SCPHF RE (CL) fuse

318 168059 CPHF Random Extension (CLS) fuse

341 177623 4,4,4-Restricted SCPHF RE (CL) fuse

361 180017 4,4-Restricted SCPHF RE (CL) fuse

418 182411 4-Restricted SCPHF RE (CL) fuse

447 184469 3-Restricted SCPHF RE (CL) fuse

451 184763 2-Restricted SCPHF RE (CL) fuse

454 184805 SCPHF Random Extension (CLS) fuse

455 184865 CPHF Random Extension (CLS) fuse

495 194423 4,4,4-Restricted SCPHF RE (CL) fuse

546 196817 4,4-Restricted SCPHF RE (CL) fuse

592 199211 4-Restricted SCPHF RE (CL) fuse

628 201269 3-Restricted SCPHF RE (CL) fuse

660 201563 2-Restricted SCPHF RE (CL) fuse

661 201605 SCPHF Random Extension (CLS) fuse

679 211223 4,4,4-Restricted SCPHF RE (CL) fuse

702 213617 4,4-Restricted SCPHF RE (CL) fuse

703 258257 Add 1 factors

704 280037 Add 2 factors

706 308593 Add 4 factors

707 312538 Add 5 factors

709 338441 Add 7 factors

722 360760 Martirosyan-Colbourn

836 363154 Martirosyan-Colbourn

894 365212 Martirosyan-Colbourn

902 365506 Martirosyan-Colbourn

908 365548 Martirosyan-Colbourn

910 365608 Martirosyan-Colbourn

990 375166 Martirosyan-Colbourn

1092 377560 Martirosyan-Colbourn

1184 379954 Martirosyan-Colbourn

1256 382012 Martirosyan-Colbourn

1320 382306 Martirosyan-Colbourn

1322 382348 Martirosyan-Colbourn

1358 391966 Martirosyan-Colbourn

1404 394360 Martirosyan-Colbourn

1406 439000 Martirosyan-Colbourn

1408 460780 Martirosyan-Colbourn

1412 489336 Martirosyan-Colbourn

1414 493281 Martirosyan-Colbourn

1418 519184 Martirosyan-Colbourn

1444 541503 Martirosyan-Colbourn

1672 543897 Martirosyan-Colbourn

1788 545955 Martirosyan-Colbourn

1804 546249 Martirosyan-Colbourn

1816 546291 Martirosyan-Colbourn

1820 546351 Martirosyan-Colbourn

1980 555909 Martirosyan-Colbourn

2184 558303 Martirosyan-Colbourn

2368 560697 Martirosyan-Colbourn

2512 562755 Martirosyan-Colbourn

2640 563049 Martirosyan-Colbourn

2644 563091 Martirosyan-Colbourn

2716 572709 Martirosyan-Colbourn

2808 575103 Martirosyan-Colbourn

2812 619743 Martirosyan-Colbourn

2814 641523 Martirosyan-Colbourn

2815 706773 Add 1 factors

2816 732513 Add 2 factors

2817 748363 Add 5 factors

2818 765802 Add 4 factors

2819 770143 Add 5 factors

2821 801669 Add 7 factors

2960 803014 perfect hash family4,3125,625T33

3125 805072 perfect hash family4,3125,625

3164 849674 Power CZ3-23.1-22.7-21.13

3264 849788 Power CZ3-23.0-22.9-21.12

3314 851096 Power CZ3-23.1-22.8-21.12

3419 851210 Power CZ3-23.0-22.10-21.11

3471 852518 Power CZ3-23.1-22.9-21.11

3581 852697 Power CZ3-23.0-22.11-21.10

3636 854005 Power CZ3-23.1-22.10-21.10

3751 854184 Power CZ3-23.0-22.12-21.9

3809 855492 Power CZ3-23.1-22.11-21.9

3929 855671 Power CZ3-23.0-22.13-21.8

3990 856979 Power CZ3-23.1-22.12-21.8

4116 857158 Power CZ3-23.0-22.14-21.7

4180 858466 Power CZ3-23.1-22.13-21.7

4311 858645 Power CZ3-23.0-22.15-21.6

4379 859953 Power CZ3-23.1-22.14-21.6

4516 860132 Power CZ3-23.0-22.16-21.5

4587 861440 Power CZ3-23.1-22.15-21.5

4731 861619 Power CZ3-23.0-22.17-21.4

4805 862927 Power CZ3-23.1-22.16-21.4

4956 863106 Power CZ3-23.0-22.18-21.3

5033 864414 Power CZ3-23.1-22.17-21.3

5192 864593 Power CZ3-23.0-22.19-21.2

5272 865901 Power CZ3-23.1-22.18-21.2

5439 866753 Power CZ3-23.0-22.20-21.1

5523 867473 Power CZ3-23.1-22.19-21.1

5628 868781 Power CZ3-23.2-22.18-21.1

5698 868913 Power CZ3-23.0-22.21

5786 869633 Power CZ3-23.1-22.20

5896 870353 Power CZ3-23.2-22.19

5901 871427 Power CZ3-23.4-22.16-21.1

6028 871661 Power CZ3-23.3-22.18

6069 872765 Power CZ3-23.5-22.15-21.1

6182 872969 Power CZ3-23.4-22.17

6258 874109 Power CZ3-23.6-22.14-21.1

6358 874307 Power CZ3-23.5-22.16

6395 875261 Power CZ3-23.8-22.11-21.2

6468 875453 Power CZ3-23.7-22.13-21.1

6556 875645 Power CZ3-23.6-22.15

6583 876462 Power CZ3-23.10-22.8-21.3

6636 876605 Power CZ3-23.9-22.10-21.2

6699 876797 Power CZ3-23.8-22.12-21.1

6776 876989 Power CZ3-23.7-22.14

6783 877634 Power CZ3-23.13-22.3-21.5

6814 877693 Power CZ3-23.12-22.5-21.4

6851 877806 Power CZ3-23.11-22.7-21.3

6896 877949 Power CZ3-23.10-22.9-21.2

6951 878141 Power CZ3-23.9-22.11-21.1

7018 878333 Power CZ3-23.8-22.13

7058 878997 Power CZ3-23.15-22.0-21.6

7080 879032 Power CZ3-23.14-22.2-21.5

7106 879067 Power CZ3-23.13-22.4-21.4

7138 879150 Power CZ3-23.12-22.6-21.3

7177 879293 Power CZ3-23.11-22.8-21.2

7224 879485 Power CZ3-23.10-22.10-21.1

7282 879677 Power CZ3-23.9-22.12

7308 880244 Power CZ3-23.14-22.6-18.1

7394 880430 Power CZ3-23.15-22.1-21.5

7417 880465 Power CZ3-23.14-22.3-21.4

7444 880524 Power CZ3-23.13-22.5-21.3

7477 880637 Power CZ3-23.12-22.7-21.2

7518 880829 Power CZ3-23.11-22.9-21.1

7568 881021 Power CZ3-23.10-22.11

7581 881549 Power CZ3-23.18-19.1-19.1-21.1

7632 881618 Power CZ3-23.15-22.5-18.1

7726 881828 Power CZ3-23.16-22.0-21.5

7746 881863 Power CZ3-23.15-22.2-21.4

7770 881898 Power CZ3-23.14-22.4-21.3

7798 881981 Power CZ3-23.13-22.6-21.2

7833 882173 Power CZ3-23.12-22.8-21.1

7876 882365 Power CZ3-23.11-22.10

7938 882824 Power CZ3-23.18-18.1-21.1-21.1

7974 882992 Power CZ3-23.16-22.4-18.1

7980 883057 Power CZ3-23.18-19.1-20.1-21.1

8000 883127 Power CZ3-23.18-20.1-20.1-20.1

8093 883261 Power CZ3-23.16-22.1-21.4

8114 883296 Power CZ3-23.15-22.3-21.3

8139 883355 Power CZ3-23.14-22.5-21.2

8169 883517 Power CZ3-23.13-22.7-21.1

8206 883709 Power CZ3-23.12-22.9

8211 884016 Power CZ3-23.19-17.1-21.1

8228 884100 Power CZ3-23.18-22.2-17.1

8280 884266 Power CZ3-23.19-18.1-20.1

8316 884306 Power CZ3-23.18-18.1-21.1-22.1

8334 884390 Power CZ3-23.17-22.3-18.1

8379 884495 Power CZ3-23.18-19.1-21.1-21.1

8400 884565 Power CZ3-23.18-20.1-20.1-21.1

8459 884659 Power CZ3-23.17-22.0-21.4

8478 884694 Power CZ3-23.16-22.2-21.3

8500 884729 Power CZ3-23.15-22.4-21.2

8526 884861 Power CZ3-23.14-22.6-21.1

8558 885053 Power CZ3-23.13-22.8

8602 885498 Power CZ3-23.19-17.1-22.1

8694 885704 Power CZ3-23.19-18.1-21.1

8712 885788 Power CZ3-23.18-22.2-18.1

8740 885937 Power CZ3-23.19-19.1-20.1

8778 885977 Power CZ3-23.18-19.1-21.1-22.1

8820 886003 Power CZ3-23.18-20.1-21.1-21.1

8861 886092 Power CZ3-23.17-22.1-21.3

8881 886127 Power CZ3-23.16-22.3-21.2

8904 886235 Power CZ3-23.15-22.5-21.1

8932 886397 Power CZ3-23.14-22.7

8993 886896 Power CZ3-23.20-17.1

9108 887186 Power CZ3-23.19-18.1-22.1

9177 887375 Power CZ3-23.19-19.1-21.1

9200 887445 Power CZ3-23.19-20.1-20.1

9240 887485 Power CZ3-23.18-20.1-21.1-22.1

9261 887490 Power CZ3-23.18-22.0-21.3

9282 887525 Power CZ3-23.17-22.2-21.2

9303 887609 Power CZ3-23.16-22.4-21.1

9328 887741 Power CZ3-23.15-22.6

9522 888584 Power CZ3-23.20-18.1

9614 888857 Power CZ3-23.19-19.1-22.1

9660 888883 Power CZ3-23.19-20.1-21.1

9702 888923 Power CZ3-23.18-22.1-21.2

9723 889007 Power CZ3-23.17-22.3-21.1

9746 889115 Power CZ3-23.16-22.5

10000 890255 Power CZ3-23.20-19.1

Graph: