Negative Latin Square Type Partial Difference Sets in Nonabelian Groups of Order 64

TL;DR

This paper catalogs 176 inequivalent negative Latin square type partial difference sets in 48 nonabelian groups of order 64, leading to 8 strongly regular graphs, using theoretical methods and exhaustive computer search.

Contribution

It provides the first extensive list of NLST PDSs in nonabelian groups of order 64, combining theoretical insights with computational enumeration.

Findings

176 inequivalent NLST PDSs identified

8 nonisomorphic strongly regular graphs constructed

Exhaustive search on 212 of 267 nonisomorphic groups of order 64

Abstract

There exist few examples of negative Latin square type partial difference sets (NLST PDSs) in nonabelian groups. We present a list of 176 inequivalent NLST PDSs in 48 nonisomorphic, nonabelian groups of order 64. These NLST PDSs form 8 nonisomorphic strongly regular graphs. These PDSs were constructed using a combination of theoretical techniques and computer search, both of which are described. The search was run exhaustively on 212/267 nonisomorphic groups of order 64.