Asymptotic Nonexistence of Difference Sets in Dihedral Groups

We prove that for any primes p1,…,ps there are only finitely many numbers ∏i=1spiαi,αi∈Z+, which can be orders of dihedral difference sets. We show that, with the possible exception of n=540, 225, there is no difference set of order n with 1<n⩽106 in any dihedral group.