SSD(27, 3^25) via Theorem 4 (n=3, s=3)

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

Note: The overall A2 value is 24; the possible projected A2 values are 0 and 2/3 with frequencies 264 and 36.  
The first column is orthogonal to all other columns.