By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square type partial difference sets in groups of the form mathbb Z32 ×mathbb Zp4t{mathbb {Z}_3^2 times mathbb {Z}_p^{4t}} where p is any odd prime. One of these families has the well-known Paley parameters, which had previously only been constructed in p-groups. This provides new constructions of Hadamard matrices and implies the existence of many new strongly regular graphs including some that are conference graphs. As a corollary, we are able to construct Paley–Hadamard difference sets of the Stanton-Sprott family in groups of the form mathbb Z32 ×mathbb Zp4t ×EA (9p4t ±2){mathbb {Z}_3^2 times mathbb {Z}_p^{4t} times {it EA} (9p^{4t} pm 2)} when 9p4t ±2{9p^{4t} pm 2} is a prime power. These are new parameters for such difference sets.
展开▼
