Transposed SSD(27, 3^169) and SSD(27, 3^156) via Theorems 6 and 7 (n=3, s=3, k=13)

0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
0 0 0 1 1 1 2 2 2 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0 0 0
0 0 0 1 1 1 2 2 2 2 2 2 0 0 0 1 1 1 0 0 0 1 1 1 2 2 2
0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 2 2 2 0 0 0 1 1 1
0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
0 1 2 1 2 0 2 0 1 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1 0 1 2
0 1 2 2 0 1 1 2 0 1 2 0 0 1 2 2 0 1 1 2 0 0 1 2 2 0 1
0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 2 0 1 0 1 2 0 1 2 0 1 2
0 1 2 1 2 0 2 0 1 2 0 1 0 1 2 1 2 0 0 1 2 1 2 0 2 0 1
0 1 2 2 0 1 1 2 0 2 0 1 1 2 0 0 1 2 0 1 2 2 0 1 1 2 0
0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 2 0 1
0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1 2 0 1 0 1 2 1 2 0
0 1 2 2 0 1 1 2 0 0 1 2 2 0 1 1 2 0 2 0 1 1 2 0 0 1 2
0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2
0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0
0 0 0 2 2 2 0 0 0 1 1 1 0 0 0 1 1 1 2 2 2 1 1 1 2 2 2
0 0 0 0 0 0 2 2 2 1 1 1 1 1 1 0 0 0 2 2 2 2 2 2 1 1 1
0 1 2 1 2 0 1 2 0 0 1 2 1 2 0 1 2 0 0 1 2 1 2 0 1 2 0
0 1 2 1 2 0 1 2 0 1 2 0 2 0 1 2 0 1 2 0 1 0 1 2 0 1 2
0 1 2 1 2 0 1 2 0 2 0 1 0 1 2 0 1 2 1 2 0 2 0 1 2 0 1
0 1 2 2 0 1 0 1 2 0 1 2 2 0 1 0 1 2 0 1 2 2 0 1 0 1 2
0 1 2 2 0 1 0 1 2 1 2 0 0 1 2 1 2 0 2 0 1 1 2 0 2 0 1
0 1 2 2 0 1 0 1 2 2 0 1 1 2 0 2 0 1 1 2 0 0 1 2 1 2 0
0 1 2 0 1 2 2 0 1 0 1 2 0 1 2 2 0 1 0 1 2 0 1 2 2 0 1
0 1 2 0 1 2 2 0 1 1 2 0 1 2 0 0 1 2 2 0 1 2 0 1 1 2 0
0 1 2 0 1 2 2 0 1 2 0 1 2 0 1 1 2 0 1 2 0 1 2 0 0 1 2
0 0 0 1 1 1 2 2 2 1 1 1 2 2 2 0 0 0 2 2 2 0 0 0 1 1 1
0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 0 0 0 2 2 2 0 0 0
0 0 0 2 2 2 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1
0 0 0 0 0 0 2 2 2 1 1 1 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2
0 1 2 1 2 0 1 2 0 1 2 0 1 2 0 0 1 2 1 2 0 0 1 2 1 2 0
0 1 2 1 2 0 1 2 0 2 0 1 2 0 1 1 2 0 0 1 2 2 0 1 0 1 2
0 1 2 1 2 0 1 2 0 0 1 2 0 1 2 2 0 1 2 0 1 1 2 0 2 0 1
0 1 2 2 0 1 0 1 2 2 0 1 0 1 2 0 1 2 0 1 2 0 1 2 2 0 1
0 1 2 2 0 1 0 1 2 0 1 2 1 2 0 1 2 0 2 0 1 2 0 1 1 2 0
0 1 2 2 0 1 0 1 2 1 2 0 2 0 1 2 0 1 1 2 0 1 2 0 0 1 2
0 1 2 0 1 2 2 0 1 0 1 2 2 0 1 0 1 2 2 0 1 0 1 2 0 1 2
0 1 2 0 1 2 2 0 1 1 2 0 0 1 2 1 2 0 1 2 0 2 0 1 2 0 1
0 1 2 0 1 2 2 0 1 2 0 1 1 2 0 2 0 1 0 1 2 1 2 0 1 2 0
0 0 0 1 1 1 2 2 2 2 2 2 0 0 0 1 1 1 1 1 1 2 2 2 0 0 0
0 0 0 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 0 0 0 0 0 0 2 2 2
0 0 0 2 2 2 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 2 2 2 2 2 2
0 0 0 0 0 0 2 2 2 0 0 0 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2
0 1 2 1 2 0 1 2 0 1 2 0 0 1 2 1 2 0 1 2 0 1 2 0 0 1 2
0 1 2 1 2 0 1 2 0 2 0 1 1 2 0 2 0 1 0 1 2 0 1 2 2 0 1
0 1 2 1 2 0 1 2 0 0 1 2 2 0 1 0 1 2 2 0 1 2 0 1 1 2 0
0 1 2 2 0 1 0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 0 1 2 0 1 2
0 1 2 2 0 1 0 1 2 1 2 0 1 2 0 0 1 2 1 2 0 2 0 1 2 0 1
0 1 2 2 0 1 0 1 2 2 0 1 2 0 1 1 2 0 0 1 2 1 2 0 1 2 0
0 1 2 0 1 2 2 0 1 2 0 1 0 1 2 0 1 2 0 1 2 2 0 1 0 1 2
0 1 2 0 1 2 2 0 1 0 1 2 1 2 0 1 2 0 2 0 1 1 2 0 2 0 1
0 1 2 0 1 2 2 0 1 1 2 0 2 0 1 2 0 1 1 2 0 0 1 2 1 2 0
0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
0 1 1 0 1 1 0 1 1 1 2 2 1 2 2 1 2 2 2 0 0 2 0 0 2 0 0
0 2 0 0 2 0 0 2 0 1 0 1 1 0 1 1 0 1 2 1 2 2 1 2 2 1 2
0 0 2 0 0 2 0 0 2 1 1 0 1 1 0 1 1 0 2 2 1 2 2 1 2 2 1
0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0 0
0 1 1 1 2 2 2 0 0 1 2 2 2 0 0 0 1 1 2 0 0 0 1 1 1 2 2
0 1 1 1 2 2 2 0 0 2 0 0 0 1 1 1 2 2 1 2 2 2 0 0 0 1 1
0 2 0 1 0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1 0 1 2 1 2
0 2 0 1 0 1 2 1 2 1 0 1 2 1 2 0 2 0 2 1 2 0 2 0 1 0 1
0 2 0 1 0 1 2 1 2 2 1 2 0 2 0 1 0 1 1 0 1 2 1 2 0 2 0
0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1
0 0 2 1 1 0 2 2 1 1 1 0 2 2 1 0 0 2 2 2 1 0 0 2 1 1 0
0 0 2 1 1 0 2 2 1 2 2 1 0 0 2 1 1 0 1 1 0 2 2 1 0 0 2
0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1
0 1 1 1 1 0 1 0 1 1 2 2 2 2 1 2 1 2 2 0 0 0 0 2 0 2 0
0 2 0 2 0 0 0 0 2 1 0 1 0 1 1 1 1 0 2 1 2 1 2 2 2 2 1
0 0 2 0 2 0 2 0 0 1 1 0 1 0 1 0 1 1 2 2 1 2 1 2 1 2 2
0 1 1 2 2 1 0 2 0 0 1 1 2 2 1 0 2 0 0 1 1 2 2 1 0 2 0
0 1 1 2 2 1 0 2 0 1 2 2 0 0 2 1 0 1 2 0 0 1 1 0 2 1 2
0 1 1 2 2 1 0 2 0 2 0 0 1 1 0 2 1 2 1 2 2 0 0 2 1 0 1
0 2 0 0 1 1 2 2 1 0 2 0 0 1 1 2 2 1 0 2 0 0 1 1 2 2 1
0 2 0 0 1 1 2 2 1 1 0 1 1 2 2 0 0 2 2 1 2 2 0 0 1 1 0
0 2 0 0 1 1 2 2 1 2 1 2 2 0 0 1 1 0 1 0 1 1 2 2 0 0 2
0 0 2 1 0 1 1 2 2 0 0 2 1 0 1 1 2 2 0 0 2 1 0 1 1 2 2
0 0 2 1 0 1 1 2 2 1 1 0 2 1 2 2 0 0 2 2 1 0 2 0 0 1 1
0 0 2 1 0 1 1 2 2 2 2 1 0 2 0 0 1 1 1 1 0 2 1 2 2 0 0
0 1 2 2 0 1 1 2 0 0 1 2 2 0 1 1 2 0 0 1 2 2 0 1 1 2 0
0 1 1 1 0 1 1 1 0 1 2 2 2 1 2 2 2 1 2 0 0 0 2 0 0 0 2
0 2 0 0 0 2 2 0 0 1 0 1 1 1 0 0 1 1 2 1 2 2 2 1 1 2 2
0 0 2 2 0 0 0 2 0 1 1 0 0 1 1 1 0 1 2 2 1 1 2 2 2 1 2
0 1 1 2 1 2 0 0 2 0 1 1 2 1 2 0 0 2 0 1 1 2 1 2 0 0 2
0 1 1 2 1 2 0 0 2 1 2 2 0 2 0 1 1 0 2 0 0 1 0 1 2 2 1
0 1 1 2 1 2 0 0 2 2 0 0 1 0 1 2 2 1 1 2 2 0 2 0 1 1 0
0 2 0 1 1 0 1 2 2 0 2 0 1 1 0 1 2 2 0 2 0 1 1 0 1 2 2
0 2 0 1 1 0 1 2 2 1 0 1 2 2 1 2 0 0 2 1 2 0 0 2 0 1 1
0 2 0 1 1 0 1 2 2 2 1 2 0 0 2 0 1 1 1 0 1 2 2 1 2 0 0
0 0 2 0 1 1 2 1 2 0 0 2 0 1 1 2 1 2 0 0 2 0 1 1 2 1 2
0 0 2 0 1 1 2 1 2 1 1 0 1 2 2 0 2 0 2 2 1 2 0 0 1 0 1
0 0 2 0 1 1 2 1 2 2 2 1 2 0 0 1 0 1 1 1 0 1 2 2 0 2 0
0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 1 2 0 2 0 1 2 0 1 2 0 1
0 1 1 0 1 1 0 1 1 2 2 1 2 2 1 2 2 1 0 2 0 0 2 0 0 2 0
0 2 0 0 2 0 0 2 0 0 1 1 0 1 1 0 1 1 2 2 1 2 2 1 2 2 1
0 0 2 0 0 2 0 0 2 1 0 1 1 0 1 1 0 1 1 2 2 1 2 2 1 2 2
0 1 1 1 2 2 2 0 0 1 1 0 2 2 1 0 0 2 1 0 1 2 1 2 0 2 0
0 1 1 1 2 2 2 0 0 2 2 1 0 0 2 1 1 0 0 2 0 1 0 1 2 1 2
0 1 1 1 2 2 2 0 0 0 0 2 1 1 0 2 2 1 2 1 2 0 2 0 1 0 1
0 2 0 1 0 1 2 1 2 2 0 0 0 1 1 1 2 2 0 0 2 1 1 0 2 2 1
0 2 0 1 0 1 2 1 2 0 1 1 1 2 2 2 0 0 2 2 1 0 0 2 1 1 0
0 2 0 1 0 1 2 1 2 1 2 2 2 0 0 0 1 1 1 1 0 2 2 1 0 0 2
0 0 2 1 1 0 2 2 1 0 2 0 1 0 1 2 1 2 2 0 0 0 1 1 1 2 2
0 0 2 1 1 0 2 2 1 1 0 1 2 1 2 0 2 0 1 2 2 2 0 0 0 1 1
0 0 2 1 1 0 2 2 1 2 1 2 0 2 0 1 0 1 0 1 1 1 2 2 2 0 0
0 1 2 1 2 0 2 0 1 1 2 0 2 0 1 0 1 2 2 0 1 0 1 2 1 2 0
0 1 1 1 1 0 1 0 1 2 2 1 2 1 2 1 2 2 0 2 0 2 0 0 0 0 2
0 2 0 2 0 0 0 0 2 0 1 1 1 1 0 1 0 1 2 2 1 2 1 2 1 2 2
0 0 2 0 2 0 2 0 0 1 0 1 0 1 1 1 1 0 1 2 2 2 2 1 2 1 2
0 1 1 2 2 1 0 2 0 1 1 0 2 1 2 2 0 0 1 0 1 1 2 2 0 0 2
0 1 1 2 2 1 0 2 0 2 2 1 0 2 0 0 1 1 0 2 0 0 1 1 2 2 1
0 1 1 2 2 1 0 2 0 0 0 2 1 0 1 1 2 2 2 1 2 2 0 0 1 1 0
0 2 0 0 1 1 2 2 1 2 0 0 1 1 0 2 1 2 0 0 2 1 0 1 1 2 2
0 2 0 0 1 1 2 2 1 0 1 1 2 2 1 0 2 0 2 2 1 0 2 0 0 1 1
0 2 0 0 1 1 2 2 1 1 2 2 0 0 2 1 0 1 1 1 0 2 1 2 2 0 0
0 0 2 1 0 1 1 2 2 0 2 0 0 1 1 2 2 1 2 0 0 1 1 0 2 1 2
0 0 2 1 0 1 1 2 2 1 0 1 1 2 2 0 0 2 1 2 2 0 0 2 1 0 1
0 0 2 1 0 1 1 2 2 2 1 2 2 0 0 1 1 0 0 1 1 2 2 1 0 2 0
0 1 2 2 0 1 1 2 0 1 2 0 0 1 2 2 0 1 2 0 1 1 2 0 0 1 2
0 1 1 1 0 1 1 1 0 2 2 1 1 2 2 2 1 2 0 2 0 0 0 2 2 0 0
0 2 0 0 0 2 2 0 0 0 1 1 1 0 1 1 1 0 2 2 1 1 2 2 2 1 2
0 0 2 2 0 0 0 2 0 1 0 1 1 1 0 0 1 1 1 2 2 2 1 2 2 2 1
0 1 1 2 1 2 0 0 2 1 1 0 1 2 2 0 2 0 1 0 1 2 2 1 2 0 0
0 1 1 2 1 2 0 0 2 2 2 1 2 0 0 1 0 1 0 2 0 1 1 0 1 2 2
0 1 1 2 1 2 0 0 2 0 0 2 0 1 1 2 1 2 2 1 2 0 0 2 0 1 1
0 2 0 1 1 0 1 2 2 2 0 0 1 0 1 2 2 1 0 0 2 0 1 1 2 1 2
0 2 0 1 1 0 1 2 2 0 1 1 2 1 2 0 0 2 2 2 1 2 0 0 1 0 1
0 2 0 1 1 0 1 2 2 1 2 2 0 2 0 1 1 0 1 1 0 1 2 2 0 2 0
0 0 2 0 1 1 2 1 2 0 2 0 1 1 0 1 2 2 2 0 0 1 0 1 2 2 1
0 0 2 0 1 1 2 1 2 1 0 1 2 2 1 2 0 0 1 2 2 0 2 0 1 1 0
0 0 2 0 1 1 2 1 2 2 1 2 0 0 2 0 1 1 0 1 1 2 1 2 0 0 2
0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 2 0 1 1 2 0 1 2 0 1 2 0
0 1 1 0 1 1 0 1 1 2 1 2 2 1 2 2 1 2 0 0 2 0 0 2 0 0 2
0 2 0 0 2 0 0 2 0 1 1 0 1 1 0 1 1 0 1 2 2 1 2 2 1 2 2
0 0 2 0 0 2 0 0 2 0 1 1 0 1 1 0 1 1 2 1 2 2 1 2 2 1 2
0 1 1 1 2 2 2 0 0 1 0 1 2 1 2 0 2 0 1 1 0 2 2 1 0 0 2
0 1 1 1 2 2 2 0 0 2 1 2 0 2 0 1 0 1 0 0 2 1 1 0 2 2 1
0 1 1 1 2 2 2 0 0 0 2 0 1 0 1 2 1 2 2 2 1 0 0 2 1 1 0
0 2 0 1 0 1 2 1 2 0 0 2 1 1 0 2 2 1 2 0 0 0 1 1 1 2 2
0 2 0 1 0 1 2 1 2 1 1 0 2 2 1 0 0 2 1 2 2 2 0 0 0 1 1
0 2 0 1 0 1 2 1 2 2 2 1 0 0 2 1 1 0 0 1 1 1 2 2 2 0 0
0 0 2 1 1 0 2 2 1 2 0 0 0 1 1 1 2 2 0 2 0 1 0 1 2 1 2
0 0 2 1 1 0 2 2 1 0 1 1 1 2 2 2 0 0 2 1 2 0 2 0 1 0 1
0 0 2 1 1 0 2 2 1 1 2 2 2 0 0 0 1 1 1 0 1 2 1 2 0 2 0
0 1 2 1 2 0 2 0 1 2 0 1 0 1 2 1 2 0 1 2 0 2 0 1 0 1 2
0 1 1 1 1 0 1 0 1 2 1 2 1 2 2 2 2 1 0 0 2 0 2 0 2 0 0
0 2 0 2 0 0 0 0 2 1 1 0 1 0 1 0 1 1 1 2 2 2 2 1 2 1 2
0 0 2 0 2 0 2 0 0 0 1 1 1 1 0 1 0 1 2 1 2 1 2 2 2 2 1
0 1 1 2 2 1 0 2 0 1 0 1 1 2 2 0 0 2 1 1 0 2 1 2 2 0 0
0 1 1 2 2 1 0 2 0 2 1 2 2 0 0 1 1 0 0 0 2 1 0 1 1 2 2
0 1 1 2 2 1 0 2 0 0 2 0 0 1 1 2 2 1 2 2 1 0 2 0 0 1 1
0 2 0 0 1 1 2 2 1 0 0 2 1 0 1 1 2 2 2 0 0 1 1 0 2 1 2
0 2 0 0 1 1 2 2 1 1 1 0 2 1 2 2 0 0 1 2 2 0 0 2 1 0 1
0 2 0 0 1 1 2 2 1 2 2 1 0 2 0 0 1 1 0 1 1 2 2 1 0 2 0
0 0 2 1 0 1 1 2 2 2 0 0 1 1 0 2 1 2 0 2 0 0 1 1 2 2 1
0 0 2 1 0 1 1 2 2 0 1 1 2 2 1 0 2 0 2 1 2 2 0 0 1 1 0
0 0 2 1 0 1 1 2 2 1 2 2 0 0 2 1 0 1 1 0 1 1 2 2 0 0 2
0 1 2 2 0 1 1 2 0 2 0 1 1 2 0 0 1 2 1 2 0 0 1 2 2 0 1
0 1 1 1 0 1 1 1 0 2 1 2 2 2 1 1 2 2 0 0 2 2 0 0 0 2 0
0 2 0 0 0 2 2 0 0 1 1 0 0 1 1 1 0 1 1 2 2 2 1 2 2 2 1
0 0 2 2 0 0 0 2 0 0 1 1 1 0 1 1 1 0 2 1 2 2 2 1 1 2 2
0 1 1 2 1 2 0 0 2 1 0 1 2 2 1 2 0 0 1 1 0 1 2 2 0 2 0
0 1 1 2 1 2 0 0 2 2 1 2 0 0 2 0 1 1 0 0 2 0 1 1 2 1 2
0 1 1 2 1 2 0 0 2 0 2 0 1 1 0 1 2 2 2 2 1 2 0 0 1 0 1
0 2 0 1 1 0 1 2 2 0 0 2 0 1 1 2 1 2 2 0 0 1 0 1 2 2 1
0 2 0 1 1 0 1 2 2 1 1 0 1 2 2 0 2 0 1 2 2 0 2 0 1 1 0
0 2 0 1 1 0 1 2 2 2 2 1 2 0 0 1 0 1 0 1 1 2 1 2 0 0 2
0 0 2 0 1 1 2 1 2 2 0 0 1 0 1 2 2 1 0 2 0 1 1 0 1 2 2
0 0 2 0 1 1 2 1 2 0 1 1 2 1 2 0 0 2 2 1 2 0 0 2 0 1 1
0 0 2 0 1 1 2 1 2 1 2 2 0 2 0 1 1 0 1 0 1 2 2 1 2 0 0

Notes: (i) SSD(27, 3^169) is a juxtaposition of 13 OA(27, 13, 3, 2) with overall A2=2028. 
The possible projected A2 values are 0, 2/9, 4/9 and 2/3 with frequencies 6708, 6318, 702 and 468. 

  (ii) Columns (1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144, 157) form a regular OA(27, 13, 3, 2). 
 Removing these 13 columns yields an SSD(27, 3^156) with overall A2=1716. 
The possible projected A2 values are 0, 2/9 and 4/9 with frequencies 5070, 6318 and 702.