Strong External Difference Families and Classification of -valuations

One method of constructing (a²+1, 2, a, 1) -SEDFs (i. e. , strong external difference families) in Z₀ℂ+₁ makes use of -valuations of complete bipartite graphs K₀, ₀. We explore this approach and we provide a classification theorem which shows that all such -valuations can be constructed recursively via a sequence of ``blow-up'' operations. We also enumerate all (a²+1, 2, a, 1) -SEDFs in Z₀ℂ+₁ for a 14 and we show that all these SEDFs are equivalent to -valuations via affine transformations. Whether this holds for all a > 14 as well is an interesting open problem. We also study SEDFs in dihedral groups, where we show that two known constructions are equivalent.