Dimensional dual hyperovals with doubly transitive automorphism groups

It is shown that if a dd-dimensional dual hyperoval SS over GF(q)GF(q) has a doubly transitive automorphism group GG, then either q=2q=2 and GG is of affine type, or q=4q=4, d=2d=2 and G≅M22G≅M22 or M22.2M22.2. 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: qq is shown to be even, and the shape of GG is strongly restricted, including the case q=2q=2.