Example of cyclic diagonal Latin square of order 13:
0 1 2 3 4 5 6 7 8 9 10 11 12
2 3 4 5 6 7 8 9 10 11 12 0 1 (d=2)
4 5 6 7 8 9 10 11 12 0 1 2 3 (d=4)
6 7 8 9 10 11 12 0 1 2 3 4 5 (d=6)
8 9 10 11 12 0 1 2 3 4 5 6 7 (d=8)
10 11 12 0 1 2 3 4 5 6 7 8 9 (d=10)
12 0 1 2 3 4 5 6 7 8 9 10 11 (d=12)
1 2 3 4 5 6 7 8 9 10 11 12 0 (d=14 == 1 (mod 13))
3 4 5 6 7 8 9 10 11 12 0 1 2 (d=16 == 3 (mod 13))
5 6 7 8 9 10 11 12 0 1 2 3 4 (d=18 == 5 (mod 13))
7 8 9 10 11 12 0 1 2 3 4 5 6 (d=20 == 7 (mod 13))
9 10 11 12 0 1 2 3 4 5 6 7 8 (d=22 == 9 (mod 13))
11 12 0 1 2 3 4 5 6 7 8 9 10 (d=24 == 11 (mod 13))
Example of horizontally semicyclic diagonal Latin square of order 13:
0 1 2 3 4 5 6 7 8 9 10 11 12
2 3 4 5 6 7 8 9 10 11 12 0 1 (d=2)
4 5 6 7 8 9 10 11 12 0 1 2 3 (d=4)
9 10 11 12 0 1 2 3 4 5 6 7 8 (d=9)
7 8 9 10 11 12 0 1 2 3 4 5 6 (d=7)
12 0 1 2 3 4 5 6 7 8 9 10 11 (d=12)
3 4 5 6 7 8 9 10 11 12 0 1 2 (d=3)
11 12 0 1 2 3 4 5 6 7 8 9 10 (d=11)
6 7 8 9 10 11 12 0 1 2 3 4 5 (d=6)
1 2 3 4 5 6 7 8 9 10 11 12 0 (d=1)
5 6 7 8 9 10 11 12 0 1 2 3 4 (d=5)
10 11 12 0 1 2 3 4 5 6 7 8 9 (d=10)
8 9 10 11 12 0 1 2 3 4 5 6 7 (d=8)
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