The two smallest dsrg's (with parameters (6,2,1,0,1) and (8,4,3,1,3)) are unique, as one easily checks. Matrices are for example
001100 000011 000011 110000 110000 001100
and
00001111 00001111 01010101 10101010 01010101 10101010 11110000 11110000(Uniqueness of dsrg(8,3,2,1,1), the complement of the one above, was first shown in Hammersley [11].)
But in general there is large freedom. Here is a dsrg with parameters (10,4,2,1,2) where points come in pairs with equal in-neighbours, but there is no such pairing for out-neighbours.
0000001111 0011110000 1100110000 0000001111 0000001111 1111000000 1100000011 0011110000 0011110000 1100001100
Jørgensen [15] did an exhaustive search and finds 16 dsrg(10,4,2,1,2).
Hammersley [11] found a dsrg(15,4,2,1,1) and is inclined to believe that it is the only one. However, Jørgensen [15] determined that there are precisely 5 of these.
Table of Jørgensen's enumeration results:
| v | k | t | λ | µ | # | comment |
| 6 | 2 | 1 | 0 | 1 | 1 | |
| 8 | 3 | 2 | 1 | 1 | 1 | Hammersley [11] |
| 10 | 4 | 2 | 1 | 2 | 16 | |
| 12 | 3 | 1 | 0 | 1 | 1 | |
| 12 | 4 | 2 | 0 | 2 | 1 | |
| 12 | 5 | 3 | 2 | 2 | 20 | |
| 14 | 5 | 4 | 1 | 2 | 0 | Klin et al. [19] |
| 14 | 6 | 3 | 2 | 3 | 16495 | |
| 15 | 4 | 2 | 1 | 1 | 5 | |
| 15 | 5 | 2 | 1 | 2 | 1292 | |
| 16 | 6 | 3 | 1 | 3 | 0 | Fiedler et al. [5] |
| 16 | 7 | 5 | 4 | 2 | 1 | |
| 18 | 4 | 3 | 0 | 1 | 1 | |
| 18 | 5 | 3 | 2 | 1 | 2 | |
| 18 | 6 | 3 | 0 | 3 | 1 | |
| 20 | 4 | 1 | 0 | 1 | 1 | |
| 24 | 6 | 2 | 0 | 2 | 1 | |
More generally, Gimbert [7] showed that dsrg(k(k+1),k,1,0,1) is unique, and Jørgensen [16] extends this to: dsrg(m(m+1)t,mt, t,0,t) is unique for all positive integers m and t.