Classification of association schemes with small vertices

(Izumi Miyamoto and Akihide Hanaki)
You can see some partial result here.
order association schemes finite groups primitive noncommutative non Schurian character tables
1 1 1 1 0
0
2 1 1 1 0
0
3 2 1 2 0
0 order 3 to 10
4 4 2 1 0
0
5 3 1 3 0
0
6 8 2 1 1
0
7 4 1 4 0
0
8 21 5 1 2
0
9 12 2 2 0
0
10 13 2 2 2
0
11 4 1 4 0
0 same as Schurian
12 59 5 1 12
0
order 12
13 6 1 6 0
0 same as Schurian
14 16 2 1 2
0 order 14, 15
15 25 1 3 1
1
16 222 14 6 49
16
order 16
17 5 1 5 0
0
same as Schurian
18 95 5 1 22
2
order 18
19 7 1 7 0
1
same as Schurian
20 95 5 1 22
0
order 20
21 32 2 3 3
0
order 21
22 16 2 1 2
0
order 22
23 22 1 22 0
18
same as Schurian
24 750 15 1 242
81
order 24
25 45 2 16 0
13
order 25
26 34 2 11 4
10
order 26
27 502 5 378 10
380
order 27
28 185 4 8 22
61
order 28
29 26 1 26 0
20
same as Schurian
30 243 4 1 66
15
order 30
31
?
1

0

same as Schurian
32 18210 51 1 3581
13949
computed
33 27 1 1 0
0
computed
34 20 2 1 4
0
computed
35
?
1




36
?
14




37
?
1

0

same as Schurian
38 33 2 1 4
11
computed
39
?
2




40
?
14




Note that we omit thin schemes (finite groups) in our data.
Our association schemes are same as homogeneous coherent configurations.
The newest result is the classification of all association schemes of order 34 (2003 Oct 15).
These results were calculated by GAP and an original program written in C language.


Program used here (source file)
Elementary Functions for Association Schemes on GAP -- How To Use It (PDF File) (updated 2012/04/08)

Primitive schemes with up to 22 and 24 vertices
Classification of weakly distance-regular digraphs with up to 21 vertices (execpt for distance-regular graphs) (2000 Aug 23)
List of noncommutative schemes (2001 Aug 16)
List of primitive schemes (2001 Aug 16)
List of quasi-thin and non Schurian schemes (2004 Jul 26)
List of schemes whose thin radicals are not normal (2005 Jul 13)
List of non Schurian schemes (2005 Jul 19)

Papers about our results

hanaki@shinshu-u.ac.jp

2016/11/03