Discrete Mathematics ( IF 0.770 ) Pub Date : 2019-12-23 , DOI: 10.1016/j.disc.2019.111744 Martin E. Malandro; Ken W. Smith
Let denote the group , where is the cyclic group of order . We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in . We use our algorithm to obtain all of these PDS in for , and we obtain partial results for and . Most of these PDS are new. For we also identify group-inequivalent PDS. Our approach involves constructing tree diagrams and canonical colorings of these diagrams. Both the total number and the number of group-inequivalent PDS in appear to grow super-exponentially in . For , a typical canonical coloring represents in excess of group-inequivalent PDS, and there are precisely reversible Hadamard difference sets.