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

2022/01/11 by Brady, Andrew Charles
#05-08 #05-11 (Secondary) #05B10 (Primary) 05-04 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.04964

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.

Related

• Negative Latin square type partial difference sets in nonelementary abelian 2-groups
• Negative Latin-Square-Type Partial Difference Sets in Non-Elementary Abelian 2-Groups
• New necessary conditions for (negative) Latin square type partial difference sets in abelian groups
• Nonabelian partial difference sets constructed using abelian techniques
• Genuinely nonabelian partial difference sets