Six Constructions of Difference Families

TL;DR

This paper introduces six new methods for constructing difference families using various combinatorial objects, applicable to all finite groups, and explores their relationships and new parameter sets.

Contribution

The paper presents six novel constructions of difference families utilizing difference sets, almost difference sets, and disjoint difference families, expanding the known parameter space.

Findings

Many new difference families with novel parameters produced.

Most constructions applicable to all finite groups.

New results on intersection numbers derived.

Abstract

In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these combinatorial objects. Most of the constructions work for all finite groups. Though these constructions look simple, they produce many difference families with new parameters. In addition to the six new constructions, new results about intersection numbers are also derived.