On difference sets with small λ

2020/07/14 by Daniel M. Gordon, Gordon, Daniel M.
Engineering · #graph theory and CDMA systems

paper · doi:10.48550/arxiv.2007.07292

Abstract

In a 1989 paper \citearasu2, Arasu used an observation about multipliers to show that no (352,27,2) difference set exists in any abelian group. The proof is quite short and required no computer assistance. We show that it may be applied to a wide range of parameters (v,k,λ), particularly for small values of λ. With it a computer search was able to show that the Prime Power Conjecture is true up to order 2 ⋅ 10¹⁰, extend Hughes and Dickey's computations for λ=2 and k ≤ 5000 up to 10¹⁰, and show nonexistence for many other parameters.

Related

• Forbidden multipliers in abelian difference sets
• Non-existence of two types of partial difference sets
• On the existence of cyclic difference sets with small parameters
• Semi-regular Relative Difference Sets with Large Forbidden Subgroups
• Sets with few differences in abelian groups