Hyperovals in Steiner systems (Q1407631)

A hyperoval of an \(S(2,l,v)\) is a set of points \(N\) such that any block meets \(N\) in either 0 or 2 points. A necessary condition for the existence of an \(S(2,4,v)\) containing a hyperoval is \(v \equiv 4 \pmod{12}\). The author proves that this condition is also sufficient. He also obtains some asymptotic results about the existence of hyperovals in \(S(2,l,v)\) with large \(l\).