  Orthogonal spreads in orthogonal spaces of type $V^+(2n+2,2)$ produce large
numbers of rank $n$ dual hyperovals in orthogonal spaces of type $V^+(2n,2)$.
The construction resembles the method for obtaining symplectic spreads in
$V(2n,q)$ from orthogonal spreads in $V^+(2n+2,q)$ when $q$ is even.
