Bilinear dual hyperovals in the largest ambient spaces

Abstract

The following facts are shown for a bilinear dual hyperoval $${\mathcal {S}}$$ of rank n. The ambient space $${\mathbf {A}}({\mathcal {S}})$$ has vector dimension at most $$n(n+1)/2$$ . The dimension of $${\mathbf {A}}({\mathcal {S}})$$ is $$n(n+1)/2$$ if and only if $${\mathcal {S}}$$ is isomorphic to the Huybrechts or the Buratti–Del Fra dual hyperoval.