Negative Latin Square Type Partial Difference Sets in Nonabelian 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.
Cite
@article{arxiv.2201.04964,
title = {Negative Latin Square Type Partial Difference Sets in Nonabelian Groups of Order 64},
author = {Andrew Charles Brady},
journal= {arXiv preprint arXiv:2201.04964},
year = {2022}
}
Comments
8 pages, 0 figures. Please find the full PDS database and code at 42ABC/Nonabelian-NLST-PDSs-of-order-64-code-data on Github. Accepted for publication in Finite Fields and their Applications. Please note that section 3.6 has been corrected to reflect that the code used only checks for difference set breakdowns, and does not check whether those difference sets are reversible