Strongly regular configurations


A table of feasible parameters of proper and primitive strongly regular configurations appears in [1]. This is an on-line version of the table with links to the actual configurations. They are represented as lists of lines, where lines are k-element lists of points, and points are integers from 1 to v. The column labeled #Cf contains information on the number of strongly regular configurations up to isomorphism, and the column labeled #SCf on the number of self-dual strongly regular configurations. A number in boldface indicates that this is the exact number, otherwise it is a lower bound.

No. (vk ; λ, μ  #Cf  #SCf 
1 (103 ; 3,4)  22
2 (133 ; 2,3)  11
3 (163 ; 2,2)  11
4 (254 ; 5,6)  00
5 (365 ; 10,12)  11
6 (415 ; 9,10)  ??
7 (454 ; 3,3)  00
8 (494 ; 5,2)  00
9 (496 ; 17,20)  11
10 (507 ; 35,36)  211111
11 (616 ; 14,15)  ??
12 (636 ; 13,15)  42
13 (647 ; 26,30)  2911
14 (818 ; 37,42)  ??
15 (856 ; 11,10)  ??
16 (857 ; 20,21)  ??
17 (965 ; 4,4)  11
18 (997 ; 21,15)  ??
19 (1009 ; 50,56)  11
20 (1059 ; 51,45)  ??
21 (1138 ; 27,28)  ??
22 (1208 ; 28,24)  11
23 (1215 ; 9,2)  00
24 (1216 ; 11,6)  ??
25 (1219 ; 43,42)  ??
26 (12110 ; 65,72)  ??
27 (1259 ; 45,36)  ??
28 (1366 ; 15,4)  ??
29 (1369 ; 36,40)  ??
30 (14411 ; 82,90)  11
31 (1459 ; 35,36)  ??
32 (1538 ; 19,21)  ??
33 (1557 ; 17,9)  42
34 (1699 ; 31,30)  ??
35 (16912 ; 101,110)  ??
36 (17111 ; 73,66)  ??
37 (1756 ; 5,5)  ??
38 (18110 ; 44,45)  ??
39 (19610 ; 40,42)  ??
40 (19613 ; 122,132)  ??
41 (19613 ; 125,120)  ??

References

  1. M. Abreu, M. Funk, V. Krcadinac, D. Labbate, Strongly regular configurations, Designs, Codes and Cryptography 90 (2022), 1881-1897. https://doi.org/10.1007/s10623-022-01080-w
    Preprint available at https://arxiv.org/abs/2104.04880.

Vedran Krcadinac,