This web page gives examples achieving the S(n) values for optimum symmetric Golomb squares in my paper "Symmetric Golomb Squares" (IEEE Transactions on Information Theory to appear).

• S(2)=3 -- Exactly 1 distinct example exists.
```11
10
```
• S(3)=5 -- Exactly 1 distinct example exists.
```011
100
101
```
• S(4)=6 -- Exactly 7 distinct examples exist.
```1101
1000
0010
1000
```
• S(5)=8 -- Exactly 2 distinct examples exist.
```10011
01000
00001
10000
10100
```
• S(6)=9 -- Exactly 16 distinct examples exist.
```101100
000001
100000
100000
000010
010001
```
• S(7)=10 -- Exactly 57 distinct examples exist.
```1100100
1000001
0000000
0001010
1000000
0001000
0100000
```
• S(8)=12 -- Exactly 4 distinct examples exist.
```11000001
10001000
00100000
00000001
01000000
00000001
00000000
10010100
```
• S(9)=13 -- Exactly 20 distinct examples exist.
```100000010
000011000
000000000
000001001
010000000
010100000
000000000
100000001
000100010
```
• S(10)=15 -- Exactly 1 distinct example exists.
```0101100010
1000000000
0000000100
1000000001
1000000000
0000010000
0000000000
0010000000
1000000010
0001000001
```
• S(11)=16 -- Exactly 4 distinct examples exist.
```11000000001
10000000000
00100010000
00010000001
00000000000
00000000001
00100000100
00000000000
00000010000
00000000010
10010100000
```
• S(12)=17 -- Exactly 15 distinct examples exist.
```101001000100
000000000001
100000001000
000100000000
000010000000
100000000000
000000000000
000000000011
001000000000
100000000000
000000010000
010000010000
```
• S(13)=18 -- Exactly 44 distinct examples exist.
```1100000000000
1000000001001
0010000000000
0001000000000
0000000100000
0000000000001
0000000000000
0000100000001
0000000000000
0100000000010
0000000000000
0000000001000
0100010100001
```
• S(14)=19 -- Exactly 262 distinct examples exist.
```11000000000001
10000001001000
00100000000000
00010000000000
00000000100000
00000000000000
00000000000001
01000000000000
00001000000001
00000000000000
01000000000010
00000000000000
00000000001000
10000010100000
```
• S(15)=21 -- Exactly 2 distinct examples exist.
```001010000100100
000000000000001
100000000000000
000100000000000
100000000100000
000000000000000
000000000000100
000000010000000
000000000001000
100010000000000
000000000000000
000000001000000
100000100000000
000000000000011
010000000000010
```
• S(16)=22 -- Exactly 2 distinct examples exist.
```1000000000001001
0000100010000000
0000000000000001
0000000000000100
0100000000000000
0000001000000000
0000010000001000
0000000100000000
0100000000000000
0000000000000000
0000000000000001
0000000000000001
1000001000000000
0001000000000000
0000000000000000
1010000000110000
```
• S(17)=23 -- Exactly 3 distinct examples exist.
```10010000000100000
00000001000000101
00000000000000000
10000000000000000
00000000010000000
00000000000000000
00000000001000100
01000001000000000
00000000000000000
00001000000000000
00000010000000000
10000000000000000
00000000000010000
00000000000000000
01000010000000001
00000000000000001
01000000000000110
```
• S(18)=24 -- Exactly 22 distinct examples exist.
```101100000000000001
000000000000100000
100000000000000010
100000000000000000
000000000000000000
000001000100000001
000000100000000000
000000000000100000
000000000000000000
000001000000000010
000000000000000000
000000000000000000
010000010000000000
000000000000001000
000000000000010000
000000000000000100
001000000100000000
100001000000000000
```
• S(19)=25 -- Exactly 59 distinct examples exist.
```1010000000000100100
0000000100000000100
1000000000000000000
0000000000000000000
0000000000010000001
0000000000000001000
0000000000000000000
0100000000000000000
0000000000000000000
0000000001000000000
0000000000000000001
0000100000000000000
0000000000001000010
1000000000000000000
0000000000000000001
0000010000000000000
1100000000000000000
0000000000001000000
0000100000100010000
```
• S(20)=26 -- Exactly 106 distinct examples exist.
```11000000000000100001
10000000000000000000
00100000000000000000
00010000000000000000
00000000000000000000
00000000100010000010
00000000000000000000
00000000000000000010
00000100100000001000
00000000000000000000
00000000000000000000
00000000000000000100
00000100000000100000
00000000000000000000
10000000000010000000
00000000000000000001
00000000100000000000
00000000000100000000
00000101000000000000
10000000000000010000
```
• S(21)=27 -- Exactly 254 distinct examples exist.
```110000000100010000010
100100000000000000000
000000000000000000010
010000000000000000000
000000000000000010000
000000000000000000000
000000000010000000000
000000010000000000000
000000000000000100000
100000000000000000001
000000100000000000000
000000000000000000000
000000000000000000000
100000000000000000000
000000000000000000001
000000001000000100000
000010000000000000010
000000000000000000000
000000000000000000000
101000000000000010000
000000000100001000000
100000000000000000000
```
• S(22)=29 -- Exactly 1 distinct example exists.
```0000100000100000000100
0010000100000001000000
0100000000000000000000
0000000000000000000000
1000000000000000000000
0000000000001000000000
0000000000000010000001
0100000000000000000000
0000000000000000010000
0000000000000000000001
1000000000000000000001
0000000000000000000000
0000010000000000000000
0000000000000101000000
0000001000000000000000
0100000000000100000000
0000000000000000000100
0000000010000000000000
0000000000000000000000
1000000000000000100000
0000000000000000000000
0000001001100000000000
```