Hyperovals of H(3, q2) when q is even

For even q, a group G isomorphic to PSL(2, q) stabilizes a Baer conic inside a symplectic subquadrangle W(3, q) of H(3, q2). In this paper the action of G on points and lines of H(3, q2) is investigated. A construction is given of an infinite family of hyperovals of size 2(q3−q) of H(3, q2), with each hyperoval having the property that its automorphism group contains G. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.