Sum Covers

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Non-strict Sum Covers

Modulus	MSC	MSC-	MSC-	Equivalence	Progressions
n		CLB	msc	Classes	max	min	Singular
3	3	0	1	1	3	3	0
4	4	0	1	1	4	4	0
5	4	0	1	1	4	4	0
6	4	0	0	1	3	3	0
7	5	0	1	1	5	5	0
8	5	0	1	2	4	4	1
9	5	0	1	1	4	4	0
10	6	1	1	6	5	4	2
11	6	0	1	2	5	4	0
12	6	0	1	6	5	3	2
13	6	0	1	1	4	4	0
14	7	1	1	14	6	4	5
15	7	1	1	13	6	3	2
16	7	0	1	7	5	4	4
17	7	0	1	1	5	5	0
18	8	1	1	79	7	3	31
19	8	1	2	18	6	4	0
20	8	1	1	40	6	4	20
21	8	1	1	8	6	4	1
22	8	0	0	1	5	5	0
23	9	1	1	94	7	4	0
24	8	0	0	1	4	4	1
25	9	1	1	41	7	3	5
26	9	1	1	22	6	4	9
27	9	1	1	6	6	3	1
28	9	1	0	1	4	4	1
29	9	0	1	1	4	4	0
30	9	0	1	2	5	4	2
31	10	1	1	53	7	3	0
32	10	1	1	39	7	3	12
33	10	1	1	23	6	3	7
34	10	1	1	5	6	4	2
35	10	1	1	4	6	4	2
36	10	1	0	1	4	4	0
37	11	1	1	182	8	4	0
38	11	1	1	153	7	3	51
39	11	1	1	61	7	3	17
40	11	1	1	24	7	3	10
41	12	2	2	>=500	9	6	0
42	11	1	1	17	6	4	14
43	12	2	2	>= 500	8	5	0
44	12	2	1	>= 500	8	4	66
45	12	2	1	328	8	3	37
46	12	1	1	139	8	3	43
47	12	1	1	25	7	3	0
48	12	1	1	84	7	3	59
49	12	1	1	8	6	4	4
50	12	1	0	6	6	4	4
51	13	2	1	>= 500	9	6	1
52	12	1	0	2	4	4	2
53	12	1	0	1	4	4	0
54	13	2	1	>= 500	8	3	257

Non-Strict Covers

Modulus	msc	Deficits		Equivalence	Progressions
n		max	min	Classes	max	min	Singular
3	2	2	2	1	2	2	0
4	3	1	1	1	3	3	0
5	3	2	2	1	3	3	0
6	4	2	0	3	4	2	0
7	4	2	1	2	4	3	0
8	4	3	2	2	3	2	0
9	4	4	4	1	2	2	0
10	5	2	1	3	4	3	0
11	5	3	2	2	4	3	0
12	5	3	3	1	3	3	1
13	5	4	4	1	3	3	0
14	6	3	1	8	5	3	3
15	6	4	2	12	4	3	6
16	6	4	2	3	4	2	1
17	6	4	4	1	4	4	0
18	7	4	1	24	5	3	7
19	6	6	6	1	2	2	0
20	7	4	1	6	5	3	2
21	7	5	2	6	5	3	0
22	8	5	0	97	6	3	33
23	8	6	1	61	6	3	0
24	8	6	0	71	6	2	24
25	8	6	2	23	6	3	1
26	8	7	2	7	5	2	1
27	8	8	4	10	4	2	1
28	9	5	0	256	7	3	84
29	8	6	6	1	3	3	0
30	8	6	6	1	2	2	0
31	9	7	2	30	6	3	0
32	9	6	3	8	5	3	2
33	9	7	2	13	5	3	6
34	9	6	6	1	3	3	0
35	9	8	8	2	3	3	0
36	10	7	0	280	7	3	113
37	10	10	1	115	6	2	0
38	10	7	2	36	6	3	12
39	10	8	2	65	6	3	20
40	10	7	2	23	5	2	16
41	10	8	4	5	4	3	0
42	10	7	2	5	4	3	3
43	10	8	6	2	4	3	0
44	11	8	1	161	7	3	59
45	11	9	2	170	7	3	16
46	11	8	2	21	5	3	7
47	11	8	2	18	6	3	0
48	11	8	2	15	5	3	14
49	11	6	4	2	5	5	0
50	12	8	0	>= 500	8	4	57
51	12	8	1	>= 500	8	4	8
52	12	9	0	327	7	3	153
53	12	10	0	172	6	3	0
54	12	10	1	50	7	2	17

Example Sum Covers

Mod	Strict	Non-Strict
3	{0, 1, 2}	{0,1}
4	{0, 1, 2, 3}	{0, 1, 2}
5	{0, 1, 2, 3}	{0, 1, 2}
6	{0, 1, 2, 4}	{0, 1, 2, 4}
7	{0, 1, 2, 3, 4}	{0, 1, 2, 4}
8	{0, 1, 2, 3, 5}	{0, 1, 2, 5}
9	{0, 1, 2, 3, 6}	{0, 1, 3, 4}
10	{0, 1, 2, 3, 4, 6}	{0, 1, 2, 3, 6}
11	{0, 1, 2, 3, 4, 7}	{0, 1, 2, 3, 7}
12	{0, 1, 2, 3, 4, 8}	{0, 1, 3, 5, 6}
13	{0, 1, 2, 3, 6, 10}	{0, 1, 2, 6, 9}
14	{0, 1, 2, 3, 4, 5, 9}	{0, 1, 2, 3, 6, 10}
15	{0, 1, 2, 3, 4, 5, 10}	{0, 1, 2, 3, 7, 11}
16	{0, 1, 2, 3, 4, 7, 12}	{0, 1, 2, 4, 9, 14}
17	{0, 1, 2, 3, 4, 8, 13}	{0, 1, 2, 3, 8, 12}
18	{0, 1, 2, 3, 4, 5, 6, 12}	{0, 1, 2, 3, 4, 8, 13}
19	{0, 1, 2, 3, 4, 5, 8, 14}	{0, 1, 3, 12, 14, 15}
20	{0, 1, 2, 3, 4, 5, 9, 15}	{0, 1, 4, 6, 8, 11, 12}
21	{0, 1, 2, 3, 4, 5, 10, 16}	{0, 1, 2, 3, 8, 12, 16}
22	{0, 1, 2, 3, 4, 8, 13, 18}	{0, 1, 2, 3, 4, 8, 13, 18}
23	{0, 1, 2, 3, 4, 5, 6, 10, 17}	{0, 1, 2, 3, 4, 8, 13, 18}
24	{0, 1, 2, 4, 8, 13, 18, 22}	{0, 1, 2, 4, 8, 13, 18, 22}
25	{0, 1, 2, 3, 4, 5, 6, 12, 19}	{0, 1, 2, 3, 5, 11, 17, 23}
26	{0, 1, 2, 3, 4, 5, 9, 15, 21}	{0, 1, 2, 3, 4, 10, 15, 20}
27	{0, 1, 2, 3, 4, 5, 10, 16, 22}	{0, 1, 2, 3, 8, 12, 18, 22}
28	{0, 1, 2, 4, 8, 10, 15, 20, 26}	{0, 1, 2, 4, 8, 10, 15, 20, 26}
29	{0, 1, 2, 3, 5, 10, 16, 22, 27}	{0, 1, 2, 6, 7, 8, 17, 20}
30	{0, 1, 2, 4, 10, 15, 17, 22, 28}	{0, 1, 3, 9, 11, 12, 16, 26}
31	{0, 1, 2, 3, 4, 5, 6, 11, 18, 25}	{0, 1, 2, 3, 4, 5, 12, 18, 24}
32	{0, 1, 2, 3, 4, 5, 6, 12, 19, 26}	{0, 1, 2, 3, 4, 10, 15, 21, 26}
33	{0, 1, 2, 3, 4, 5, 10, 16, 22, 28}	{0, 1, 2, 3, 9, 13, 18, 23, 27}
34	{0, 1, 2, 3, 4, 6, 12, 19, 26, 32}	{0, 1, 2, 4, 10, 12, 13, 17, 31}
35	{0, 1, 2, 3, 5, 10, 16, 22, 28, 33}	{0, 1, 2, 7, 8, 11, 26, 29, 30}
36	{0, 1, 2, 3, 6, 12, 19, 20, 27, 33}	{0, 1, 2, 3, 6, 12, 19, 20, 27, 33}
37	{0, 1, 2, 3, 4, 5, 6, 7, 14, 22, 30}	{0, 1, 2, 3, 4, 10, 15, 20, 26, 30}
38	{0, 1, 2, 3, 4, 5, 6, 11, 18, 25, 32}	{0, 1, 2, 3, 4, 10, 16, 21, 26, 32}
39	{0, 1, 2, 3, 4, 5, 6, 12, 19, 26, 33}	{0, 1, 2, 3, 6, 11, 18, 24, 31, 36}
40	{0, 1, 2, 3, 4, 5, 10, 17, 23, 29, 33}	{0, 1, 2, 3, 4, 11, 16, 22, 28, 33}
41	{0, 1, 2, 3, 4, 5, 6, 7, 8, 15, 24, 33}	{0, 1, 2, 3, 10, 14, 19, 25, 30, 34}
42	{0, 1, 2, 3, 4, 9, 16, 20, 26, 30, 37}	{0, 1, 3, 6, 8, 9, 18, 22, 29, 33}
43	{0, 1, 2, 3, 4, 5, 6, 7, 12, 20, 28, 36}	{0, 1, 2, 6, 7, 8, 18, 21, 30, 33}
44	{0, 1, 2, 3, 4, 5, 6, 7, 13, 21, 29, 37}	{0, 1, 2, 3, 4, 5, 12, 18, 24, 31, 36}
45	{0, 1, 2, 3, 4, 5, 6, 7, 14, 22, 30, 38}	{0, 1, 2, 3, 4, 5, 12, 19, 25, 31, 38}
46	{0, 1, 2, 3, 4, 5, 6, 12, 19, 26, 33, 40}	{0, 1, 2, 3, 4, 10, 17, 22, 28, 33, 40}
47	{0, 1, 2, 3, 4, 5, 6, 12, 20, 27, 34, 39}	{0, 1, 2, 3, 4, 5, 13, 19, 26, 33, 39}
48	{0, 1, 2, 3, 4, 5, 6, 13, 21, 27, 33, 41}	{0, 1, 2, 6, 8, 17, 20, 30, 33, 42, 44}
49	{0, 1, 2, 3, 4, 5, 11, 18, 23, 31, 36, 43}	{0, 1, 2, 3, 4, 12, 17, 23, 30, 36, 41}
50	{0, 1, 2, 3, 4, 5, 11, 19, 24, 31, 36, 44}	{0, 1, 2, 3, 4, 5, 11, 19, 24, 31, 36, 44}
51	{0, 1, 2, 3, 4, 5, 6, 7, 8, 16, 26, 33, 43}	{0, 1, 2, 3, 4, 5, 6, 14, 21, 28, 36, 42}
52	{0, 1, 2, 4, 5, 6, 11, 19, 27, 31, 39, 47}	{0, 1, 2, 4, 5, 6, 11, 19, 27, 31, 39, 47}
53	{0, 1, 2, 3, 6, 11, 18, 25, 31, 38, 45, 50}	{0, 1, 2, 3, 6, 11, 18, 25, 31, 38, 45, 50}
54	{0, 1, 2, 3, 4, 5, 6, 7, 14, 23, 31, 39, 45}	{0, 1, 2, 4, 6, 12, 19, 28, 32, 37, 44, 52}

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