New parameter families of strongly regular graphs and partial difference sets

Construct strongly regular graphs and partial difference sets belonging to new parameter families distinct from the Latin square type, negative Latin square type, generalized Denniston, and dual generalized Denniston families.

Background

The generalized Denniston and dual generalized Denniston families introduced in the paper are largely distinct from the established Latin square type and negative Latin square type families. The authors identify the construction of further genuinely new parameter families as an explicit unresolved direction.