Note that, if there exists an association scheme of prime order p and class d, then d must be a divisor of p-1.

Order 40
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 (classified)
3
4 (21 days on Core i7-8700K 2018/07)
5 (21 days on Core i7-8700K 2018/07)
6 (2 months on Core i7-3970X 2013/03)
7 372 (2009/06/30) (Core2Quad:090628) computed
8 (7 days on Core i7-3970X 2012/12)
9 143 (2009/06/30) (Core2Quad:090628) computed
10 46 (2009/06/30) (Core2Quad:090628) computed
11 116 (2009/06/30) (Core2Quad:090628) computed
12 (2 months on Core i7-3970X 2013/03)
13 92 (2009/08/08) (Core2Quad:090723) computed
14 21 (2009/08/08) (Core2Quad:090723) computed
15 88 (2009/08/08) (Core2Quad:090723) computed
16 28 (2009/08/08) (Core2Quad:090723) computed
17 18 (2009/08/08) (Core2Quad:090723) computed
18 5 (2009/08/08) (Core2Quad:090723) computed
19 10 (2009/08/09) (Core2Quad:090723) computed
20 14 (2009/07/01) (Core2Quad:090628) computed
21 34 (2009/07/02) (Core2Quad:090628) computed
22 0 (2009/08/21) (Core2Quad:090723) --
23 49 2009/10/20 Core2Quad:090723 computed
24 13 (2009/08/03) (Core2Quad:090723) computed
25 -- 28 0 (2009/08/03) (Core2Quad:090723) --
29 12 (2009/08/06) (Core2Quad:090723) computed
30 -- 38 0 (2009/08/06) (Core2Quad:090723) --
39 (thin) 14 -- -- --

Order 41
(prime)
Class # isomorphism classes date machine
1 1 -- --
2 difficult
4 difficult
5 difficult
8 1 (Schurian) -- --
10 1 (Schurian) -- --
20 1 (Schurian) -- --
40 (thin) 1 -- --

Order 42
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 6 SRG on (prime + 1) points
3
4
5
6 (2 months on Core i7-3970X 2013/05)
7 30 (2009/08/22) (Core2Quad:090723) computed
8 22 (2009/08/22) (Core2Quad:090723) computed
9 (2 mounths on Core i7-3970X 2013/05)
10 0 (2009/07/17) (Core2Quad:090714) --
11 27 (2009/07/18) (Core2Quad:090714) computed
12 6 (2009/07/18) (Core2Quad:090714) computed
13 1 (2009/07/18) (Core2Quad:090714) computed
14 15 (2009/07/18) (Core2Quad:090714) computed
15 16 (2009/07/18) (Core2Quad:090714) computed
16 0 (2009/07/18) (Core2Quad:090714) --
17 12 (2009/07/18) (Core2Quad:090714) computed
18 -- 19 0 (2009/07/18) (Core2Quad:090714) --
20 3 (2009/07/19) (Core2Quad:090714) computed
21 6 2009/09/04 Core2Quad:090723 computed
22 0 (2009/07/15) (Core2Duo:090714) --
23 9 2009/07/15 Core2Duo:090714 computed
24 -- 26 0 (2009/07/15) (Core2Duo:090714) --
27 6 (2009/07/15) (Core2Duo:090714) computed
28 -- 40 0 (2009/07/15) (Core2Duo:090714) --
41 (thin) 6 -- -- --

Order 43 (prime)
Class # isomorphism classes date machine
1 1 -- --
2 difficult
3
6 1 (Schurian) (2009/06/28) (Core2Quad:090628)
7 1 (Schurian) 2005/09/08 light
14 1 (Schurian) (2009/07/06) (Core2Quad:090703)
21 1 (Schurian) (2009/09/25) (Core2Quad:090723)
42 (thin) 1 -- --

Order 44
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 4 SRG on (prime + 1) points
3
4
5 (1 hour on light 2005/6)
6 (6 hours on light 2005/6)
7 (2 months on Core i7--3970X 2013/05)
8 8 (2009/07/26) (Core2Duo:090714) computed
9 -- 10 0 (2009/07/26) (Core2Duo:090714) --
11 7 (2009/07/21) (Core2Duo:090714) computed
12 5 (2009/07/21) (Core2Duo:090714) computed
13 8 (2009/07/22) (Core2Duo:090714) computed
14 0 (2009/07/22) (Core2Duo:090714) --
15 1 (2009/07/23) (Core2Duo:090714) computed
16 0 (2009/07/23) (Core2Duo:090714) --
17 1 (2009/07/23) (Core2Duo:090714) computed
18 0 (2009/07/23) (Core2Duo:090714) --
19 1 (2009/07/23) (Core2Duo:090714) computed
20 0 -- -- --
21 1 2009/11/05 Core2Quad:090723 computed
22 6 2009/11/05 Core2Quad:090723 computed
23 10 2009/11/06 Core2Quad:090723 computed
24 -- 31 0 (2009/07/26) (Core2Duo:090714) --
32 2 (2009/07/26) (Core2Duo:090714) computed
33 -- 42 0 (2009/07/26) (Core2Duo:090714) --
43 (thin) 4 -- -- --

Order 45
Class # isomorphism classes date machine character tables
1 1 -- -- --
2
3
4
5
6
7 difficult !
8 30 2009/09/08 Core2Quad:090723 computed
9 25 2009/09/07 Core2Quad:090723 computed
10 16 (2009/09/06) (Core2Quad:090723) computed
11 (20 days on Core2Quad 2009/12)
12 16 (2009/07/09) (Core2Quad:090708) computed
13 7 (2009/07/09) (Core2Quad:090708) computed
14 10 (2009/07/09) (Core2Quad:090708) computed
15 3 (2009/07/09) (Core2Quad:090708) computed
16 3 (2009/07/09) (Core2Quad:090708) computed
17 6 (2009/07/09) (Core2Quad:090708) computed
18 0 (2009/07/10) (Core2Quad:090708) --
19 3 (2009/07/10) (Core2Quad:090708) computed
20 5 (2009/07/10) (Core2Quad:090708) computed
21 0 (2009/07/10) (Core2Quad:090708) --
22 2 2018/03/24
23 1 (2009/07/15) (Core2Quad:090708) computed
24 3 (2009/07/16) (Core2Quad:090708) computed
25 0 (2009/07/16) (Core2Quad:090708) --
26 2 2018/03/11
27 -- 28 0 (2009/09/02) (Core2Quad:090723) --
29 1 2018/03/11
30 -- 43 0 (2009/09/02) (Core2Quad:090723) --
44 (thin) 2 -- -- --

Order 46
Class # isomorphism classes date machine character tables
1 1 -- -- --
2
3
4
5
6 0 2011/06/12 (Core i3:090723) ---
7 0 2011/06/12 (Core i3:090723) ---
8 0 2011/06/12 (Core i3:090723) ---
9 (7 days on Core i7-3970X 2012/12)
10 -- 11 0 (2009/09/02) (Core2Quad:090723) --
12 2 (2009/09/02) (Core2Quad:090723) computed
13 0 (2009/09/02) (Core2Quad:090723) --
14 0 (2009/07/13) (Core2Duo:090708) --
15 (20 days on Core2Quad 2009/12)
16 -- 20 0 (2009/07/13) (Core2Duo:090708) --
21 0 2009/11/09 Core2Quad:090723 --
22 0 2012/12/11 Core i7-3970X --
23 (10 days on light 2005/7)
24 -- 44 0 (2009/08/29) (Core2Quad:090723) --
45 (thin) 2 -- -- --

Order 47 (prime)
Class # isomorphism classes date machine
1 1 -- --
2 difficult ! [Non-symmetric, AIso to Schurian]
23 1 (Schurian) -- --
46 (thin) 1 -- --

Order 48
Class # isomorphism classes date machine character tables
1 1 -- -- --
2 8 SRG on (prime + 1) points
3
4
5
6
7
8
9 (1 day on kissme, 2008/07)
10 (14 days on Core i7-8700K 2018/06)
11 (14 days on Core i7-8700K 2018/06)
12 (14 days on Core i7-8700K 2018/06)
13 (14 days on Core i7-8700K 2018/06)
14 (14 days on Core i7-8700K 2018/06)
15 (14 days on Core i7-8700K 2018/06)
16 (14 days on Core i7-8700K 2018/06)
17 (14 days on Core i7-8700K 2018/06)
18 287 (2009/07/02) (Core2Duo:090628) computed
19 1590 (2010/01/02) (Core2Quad:090723) computed
20 209 (2010/01/07) (Core2Quad:090723) computed
21 516 (2010/01/23) (Core2Quad:090723) computed
22 4 (2010/02/02) (Core2Quad:090723) computed
23 589 2010/02/01 Core2Quad:090723 computed
24 34 (2010/02/28) (Core2Quad:090723) computed
25 185 2010/04/05 Core2Quad:090723 computed
26 45 (2009/09/09) (Core2Quad:090723) computed
27
28 0 (2009/08/29) (Core2Quad:090723) --
29
30 0 (2009/08/29) (Core2Quad:090723) --
31
32 -- 34 0 (2009/08/29) (Core2Quad:090723) --
35
36 -- 46 0 (2009/08/29) (Core2Quad:090723) --
47 (thin) 52 -- -- --

Order 49
Class # isomorphism classes date machine character tables
1 1 -- -- --
2
3
4
5
6
7 (6 hours on kissme)
8 (12 hours on kissme)
9 5 (2009/07/23) (Core2Quad:090714) computed
10 1 (2009/07/22) (Core2Quad:090714) computed
11 (2 days on kissme)
12 (1 month 2018/02)
13 1 2009/07/26 Core2Quad:090714 computed
14 0 (2009/07/26) (Core2Quad:090714) --
15
16 (1 month 2018/02)
17 -- 19 0 (2009/07/16) (Core2Quad:090714) --
20 1 (2009/07/26) (Core2Quad:090714) computed
21 0 (2009/07/26) (Core2Quad:090714) --
22 0 2010/09/02 Core2Quad:090723 --
23 0 2010/09/03 Core2Quad:090723 --
24 2 2010/09/03 Core2Quad:090723 computed
25 -- 26 0 (2009/07/16) (Core2Quad:090714) --
27 1 2010/09/04 Core2Quad:090723 computed
28 -- 47 0 (2009/08/29) (Core2Quad:090723) --
48 (thin) 2 -- --