A new family of dual hyperovals in with

In 2003, a class of d -dimensional dual hyperovals was constructed by Buratti and Del Fra [M. Buratti, A. Del Fra, Semi-Boolean quadruple systems and dimensional dual hyperovals, Adv. Geom. 3 (2003) 245–253] based on Huybrechts’ dual hyperovals. We construct a family based on Veronesean dual hyperovals in PG ( d ( d + 3 ) / 2 , 2 ) . However, these dual hyperovals are not isomorphic to the Veronesean dual hyperovals and do not satisfy Property  ( T ) . Hence, we conclude that these are new dual hyperovals.