This is one of two self-complementary, rank-3 strongly-regular graphs with parameters $(81,40,19,20)$, the other being the Peisert graph on 81 vertices.
| Number of vertices: | $81$ |
| Diameter: | $2$ |
| Intersection array: | $\{40,20; 1,20\}$ |
| Spectrum: | $40^1 4^{40} (-5)^{40}$ |
| Automorphism group: | $3^4:40:4$ |
| Distance-transitive: | Yes |
| Primitive |