Hyperoval

Summary

A hyperoval in a finite projective plane of order $n$ is a set of $n + 2$ points with no three on a line. It is the largest possible size of such a set, and it can occur only when $n$ is even. When $n$ is even, every oval extends to a hyperoval by adding one point, the nucleus, where all tangents of the oval meet. The classification of hyperovals in $PG(2, 2^h)$ is a long-standing problem of finite geometry.