On this website we have six rank-3 strongly regular graphs on 1024 vertices. They are $H(2,32)$, the bilinear forms graph $\mathrm{H}_2(2,5)$, $\mathrm{VO}_{10}^-(2)$, $\mathrm{VO}_{10}^+(2)$, $\overline{\mathrm{VO}_{10}^+(2)}$, and the Alternating Forms graph below. The local graph of the graph below is the Grassmann graph $\mathrm{J}_2(5,2)$.
| Number of vertices: | $1024$ |
| Diameter: | $2$ |
| Intersection array: | $\{155,112;1,20\}$ |
| Spectrum: | $155^1 27^{155} (-5)^{868}$ |
| Automorphism group: | $2^{10}:\mathrm{PSL}(5,2)$ |
| Distance-transitive: | Yes |
| Primitive |