Nonexistence of Strong External Difference Families in Abelian Groups of Order Being Product of At Most Three Primes

Ka Hin Leung; Shuxing Li; Theo Fanuela Prabowo

paper

Nonexistence of Strong External Difference Families in Abelian Groups of Order Being Product of At Most Three Primes

arXiv:1910.03258

Abstract

Let $v$ be a product of at most three not necessarily distinct primes. We prove that there exists no strong external difference family with more than two subsets in abelian group $G$ of order $v$ , except possibly when $G = C_{p}^{3}$ and $p$ is a prime greater than $3 \times 1 0^{12}$ .

30 pages, major changes made to version 1, we refined proofs to some theorems and reorganized the exposition of many results