SGDs with doubly transitive automorphism group

Symmetric graph designs, or SGDs, were defined by Gronau et al. as a common generalization of symmetric BIBDs and orthogonal double covers. This note gives a classification of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those that admit a 3-transitive group, and those with λ = 1. The latter case includes the determination of all near 1-factorizations of Kn (partitions of the edge set into subsets each of which consists of disjoint edges covering all but one point), which admit 2-transitive groups.