On Ovoids in Orthogonal Spaces of Type \(O_5(q)\)

It is known that the ovoids in \({O}_5(q)\), \(q \leq 7\), are classical ovoids. Using algebraic and computational techniques, we classify ovoids in \({O}_5(9)\) and \({O}_5(11)\) with the aid of a computer. We also study the ovoids which contain an irreducible conic and classify them in \({O}_5(13)\). Our results show that there is only one nonclassical ovoid (a member from a family of Kantor) up to isomorphism in \({O}_5(9)\) and all the ovoids in \({O}_5(11)\) are classical.