Negative Latin square type partial difference sets in nonabelian groups of order 64 (Q2135572)

This paper describes a computational search for negative Latin square type partial difference sets in groups of order 64. The search exhaustively covered 212 of the 267 groups of order 64, namely the groups which have a homomorphism onto the elementary abelian group of order 8 (other than the elementary abelian group of order 64). The search found 176 partial difference sets up to equivalence, coming from 48 different nonabelian groups. Among those groups, there were 18 that possessed disjoint partial difference sets. There were also disjoint partial difference sets found in \(C_4^2\times C_2^2\). The partial difference sets can be used to construct 8 strongly regular graphs with parameters (64,18,2,6). A catalogue of the 167 strongly regular graphs with these parameters was found by \textit{W. H. Haemers} and \textit{E. Spence} [Eur. J. Comb. 22, No. 6, 839--845 (2001; Zbl 0983.05078)].