Hemisystems and strongly regular graphs

In a recent paper, it was constructed a family of hemisystems of H ( 3 , p 2 ) , for every prime p of the form p = 1 + 4 a 2 , stabilised by P S L ( 2 , p ) × C p + 1 2 . In the case p = 5 , the full automorphism group is 3 . A 7 , and the hemisystem is isomorphic to a sporadic one described by A. Cossidente and T. Penttila in 2005. Here, we investigate the new family of hemisystems and the related strongly regular graphs. In this way, we find a new family of strongly regular graphs, cospectral but not isomorphic to the Cossidente–Penttila graph.