Strongly regular configurations

TL;DR

This paper investigates combinatorial configurations with strongly regular point and line graphs, constructing new examples, establishing existence conditions, and analyzing feasible parameters up to 200 points.

Contribution

It introduces new strongly regular configurations beyond known classes, proves necessary existence conditions, and identifies feasible parameter sets with non-existence results.

Findings

Constructed new configurations not in known classes

Established necessary conditions for existence

Presented feasible parameter table up to 200 points

Abstract

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed. Necessary existence conditions are proved and a table of feasible parameters of such configurations with at most 200 points is presented. Non-existence of some configurations with feasible parameters is proved.