Generalized Denniston parameters beyond elementary abelian groups

Construct strongly regular Cayley graphs and partial difference sets with generalized Denniston and dual generalized Denniston parameters in groups other than elementary abelian groups.

Background

The paper constructs generalized Denniston and dual generalized Denniston strongly regular Cayley graphs and partial difference sets in elementary abelian groups. Earlier work had produced strongly regular graphs and partial difference sets with ordinary Denniston parameters in nonelementary abelian and nonabelian groups. The authors explicitly ask whether their two generalized parameter families can likewise be realized in broader classes of groups.