Dimensional dual hyperovals with doubly transitive automorphism groups

It is shown that if a d -dimensional dual hyperoval S over G F ( q ) has a doubly transitive automorphism group G , then either q = 2 and G is of affine type, or q = 4 , d = 2 and G ≅ M 22 or M 22 . 2 . This improves the results in [C. Huybrechts, A. Pasini, Flag-transitive extensions of dual affine spaces, Contrib. Algebra Geom. 40 (1999) 503–532] in the following sense: q is shown to be even, and the shape of G is strongly restricted, including the case q = 2 .