Some nonexistence results for (v,m,k,pq)-strong external difference families

In this paper, we derive some restrictions and nonexistence results for (v,m,k,pq)-strong external difference families (SEDFs), where p and q are primes. We first show that there is no abelian (v,m,k,p2)-SEDF with m>2. If p>q, we show that if q+1 is a power of two; or q+1=2r or 4r for some prime r>3, then there is no abelian (v,m,k,pq)-SEDF with m>2 for all sufficiently large primes p. Furthermore, we completely rule out the existence of abelian (v,m,k,pq)-SEDF with m>2 in case q=2,3,5,7,13,19,31.