All (96,20,4) difference sets and related structures

10.Dec.2019

In 1978, Robert Kibler at the National Security Agency in Fort Meade, Maryland published a description of all noncyclic difference sets with  . Kibler's decision to stop his extensive computer search for difference sets at block size 19 was motivated partly by the difficult barrier at  , the difference sets with parameters  . In this paper, we announce the completion of the search for all   difference sets, relying on the computer software GAP and the work of numerous authors over the last few decades. The difference sets and the symmetric designs they create are summarized and links are provided to webpages which explicitly list the difference sets. In addition, we use these   difference sets to construct all   and   partial difference sets and briefly look at the corresponding strongly regular graphs.