Symmetric Golomb Squares

IBM - Personal communication

This web page contains a table of values of S(n) where S(n) is the maximum number of ones that can be found in a symmetric (with respect to diagonal reflection) Golomb square. A Golomb square is a square Golomb Rectangle . Symmetric Golomb squares are easier to search for than general Golomb squares and are often as good. For more about this see my paper "Symmetric Golomb Squares" (IEEE Transactions on Information Theory, to appear).

Examples achieving these values can be found here .

Table of S(n) values

n S(n) Number of Squares Exhaustive Search Time
2 3 1 .00
3 5 1 .00
4 6 7 .00
5 8 2 .00
6 9 16 .00
7 10 57 .00
8 12 4 .01
9 13 20 .01
10 15 1 .01
11 16 4 .11
12 17 15 .32
13 18 44 2.19
14 19 262 6.59
15 21 2 14.65
16 22 2 102.48
17 23 3 279.41
18 24 22 1967.53
19 25 59 5365.38
20 26 106 36796.94
21 27 254 96431.68
22 29 1 174610.01

Table of S(n) values
n	S(n)	Number of Squares	Exhaustive Search Time
2	3	1	.00
3	5	1	.00
4	6	7	.00
5	8	2	.00
6	9	16	.00
7	10	57	.00
8	12	4	.01
9	13	20	.01
10	15	1	.01
11	16	4	.11
12	17	15	.32
13	18	44	2.19
14	19	262	6.59
15	21	2	14.65
16	22	2	102.48
17	23	3	279.41
18	24	22	1967.53
19	25	59	5365.38
20	26	106	36796.94
21	27	254	96431.68
22	29	1	174610.01