Some Nonexistence Results for Strong External Difference Families Using Character Theory

In this paper, we study the existence of $(v,m,k,\lambda )$-strong external difference families (SEDFs). We use character-theoretic techniques to show that no SEDF exists when $v$ is prime, $k>1$ and $m>2$. In the case where $v$ is the product of two distinct odd primes, some necessary conditions are derived, which can be used to rule out certain parameter sets. Further, we show that, when $m=3$ or $4$ and $v>m$, a $(v,m,k,\lambda )$-SEDF does not exist.