Automorphisms of graph with intersection array $\{64,42,1;1,21,64\}$

A.A. Makhnev and M.S. Samoilenko found parameters of strongly regular graphs which can be local subgraphs in antipodal distance-regular graph of diameter $3$ with $\lambda=\mu$. It is suggested the programm of investigation antipodal distance-regular graph of diameter $3$ with $\lambda=\mu$ and local subgraphs having this parameters. It is consider parameters $(64,21,8,6)$ in this paper. It is proved that vertex-symmetric distance-regular graph with intersection array $\{64,42,1;1,21,64\}$ is arc-transitive with the automorphism group having socle $L_2(64)$ or $U_3(4)$.