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 31 (prime)
Classification of schemes of class greater than 2 has been finished. All of them are Schurian. There are many schemes of class 2.

Order 32, 33, 34 : classified

Order 35

Class	# isomorphism classes	date	machine	character tables
1	1	--	--	--
2	difficult
3	difficult
4	7	(2009/08/02)	(Core2Quad:090723)	computed
5	6	(2009/06/28)	(Core2Quad:B040830)	computed
6	2	(2009/06/28)	(Core2Quad:B040830)	computed
7	6	(2009/06/28)	(Core2Quad:B040830)	computed
8	3	(2009/06/28)	(Core2Quad:B040830)	computed
9	1	(2009/06/28)	(Core2Quad:B040830)	computed
10	3	(2009/06/28)	(Core2Quad:B040830)	computed
11	1	(2009/06/28)	(Core2Quad:B040830)	computed
12	0	(2009/06/28)	(Core2Quad:B040830)	--
13	1	(2009/06/28)	(Core2Quad:B040830)	computed
14	1	(2009/06/28)	(Core2Quad:B040830)	computed
15 -- 16	0	(2009/06/28)	(Core2Quad:B040830)	--
17	1	(2009/06/28)	(Core2Quad:B040830)	computed
18	0	(2009/06/28)	(Core2Quad:B040830)	--
19	1	(2009/06/28)	(Core2Quad:B040830)	computed
20	1	(2009/06/28)	(Core2Quad:B040830)	computed
21 -- 33	0	(2009/07/30)	(Core2Quad:090723)	--
34 (thin)	1	--	--	--

Order 36

Class	# isomorphism classes	date	machine	character tables
1	1	--	--	--
2	(classified) (21 days on Core i7-8700K 2018/07)
3	(21 days on Core i7-8700K 2018/07)
4	63	2013/02/10	Core i7-3970X	computed
5	102	2013/02/07	Core i7-3970X	computed
6	109	2009/07/08	Core2Quad:090628	computed
7	162	2009/07/08	Core2Quad:090628	computed
8	173	2009/08/21	Core2Quad:090723	computed
9	152	(2009/07/21)	(Core2Duo:090714)	computed
10	160	(2009/07/21)	(Core2Duo:090714)	computed
11	141	(2009/07/20)	(Core2Duo:090714)	computed
12	71	(2009/07/20)	(Core2Duo:090714)	computed
13	77	(2009/07/20)	(Core2Duo:090714)	computed
14	42	(2009/07/20)	(Core2Duo:090714)	computed
15	73	(2009/07/20)	(Core2Duo:090714)	computed
16	0	(2009/07/20)	(Core2Duo:090714)	--
17	44	(2009/07/20)	(Core2Duo:090714)	computed
18	17	(2009/07/20)	(Core2Duo:090714)	computed
19	43	(2009/07/20)	(Core2Duo:090714)	computed
20	19	(2009/07/20)	(Core2Duo:090714)	computed
21 -- 22	0	(2009/07/20)	(Core2Duo:090714)	--
23	34	(2009/07/20)	(Core2Duo:090714)	computed
24 -- 25	0	(2009/07/20)	(Core2Duo:090714)	--
26	5	(2009/08/02)	(Core2Quad:090723)	computed
27 -- 34	0	(2009/07/30)	(Core2Quad:090723)	--
35 (thin)	14	--	--	--

Order 37 (prime)

Class	# isomorphism classes	date	machine
1	1	--	--
2	difficult
3	difficult
4	1 (schurian)	(2009/08/01)	(Core2Quad:090723)
6	1 (schurian)	(2009/08/01)	(Core2Quad:090723)
9	1 (Schurian)	(2009/08/01)	(Core2Quad:090723)
12	1 (Schurian)	(2009/08/01)	(Core2Quad:090723)
18	1 (Schurian)	(2009/08/01)	(Core2Quad:090723)
36 (thin)	1	--	--

Order 38 : classified

Order 39

Class	# isomorphism classes	date	machine	character tables
1	1	--	--	--
2	difficult
3
4	5	2013/03/15	Core i7-3970X	computed
5	6	2013/03/15	Core i7-3970X	computed
6	2	(2009/07/05)	(Core2Duo:090703)	computed
7	4	(2009/07/04)	(Core2Duo:090703)	computed
8	3	(2009/07/04)	(Core2Duo:090703)	computed
9	1	(2009/07/04)	(Core2Duo:090703)	computed
10	1	(2009/07/04)	(Core2Duo:090703)	computed
11	2	(2009/07/04)	(Core2Duo:090703)	computed
12	0	(2009/07/04)	(Core2Duo:090703)	--
13	3	(2009/07/04)	(Core2Duo:090703)	computed
14	3	(2009/07/04)	(Core2Duo:090703)	computed
15 -- 18	0	(2009/07/04)	(Core2Duo:090703)	--
19	1	(2009/07/05)	(Core2Duo:090703)	computed
20	2	(2009/07/05)	(Core2Duo:090703)	computed
21 -- 24	0	(2009/07/05)	(Core2Duo:090703)	--
25	1	(2009/07/05)	(Core2Duo:090703)	computed
26 -- 37	0	(2009/07/30)	(Core2Quad:090723)	--
38 (thin)	2	--	--	--