New negative Latin square type partial difference sets in nonelementary abelian 2-groups and 3-groups

A partial difference set having parameters (n2, r(n - 1), n + r2 - 3r, r2 - r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n+1), -n+r2 +3r, r2 +r) is called a negative Latin square type partial difference set. Nearly all known constructions of negative Latin square partial difference sets are in elementary abelian groups. In this paper, we develop three product theorems that construct negative Latin square type partial difference sets and Latin square type partial difference sets in direct products of abelian groups G and G when these groups have certain Latin square or negative Latin square type partial difference sets. Using these product theorems, we can construct negative Latin square type partial difference sets in groups of the form G = (Z2)4s0 ? (Z4)2s1 ? (Z16)4s2 ? ? ? ? ? (Z22r )4sr where

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: John B. Polhill
• Keywords: Computer Graphics, DCC 2008, Partial Difference Sets, Square Partial Difference, Type Partial Difference