The eight dimensional ovoids over GF(5) (Q2701571)

Let \(V\) be a nondegenerate orthogonal vector space over \(\text{ GF}(q)\). An ovoid is a set of isotropic points having precisely one point in common with each maximal totally singular \(r\)-space. If \(V\) has dimension \(2n\), then \(V\) is denoted by \(\Omega^+(2n,q)\) if \(r=n\) and by \(\Omega^-(2n,q)\) if \(r=n-1\). NEWLINENEWLINENEWLINEThe authors outline a computer assisted proof of the classification of all ovoids in \(\Omega^+(8,5)\). There are three classes: the unitary ovoids and two classes derived from the root lattices \(E_8\) [\textit{J. H. Conway, P. B. Kleidman} and \textit{R. A. Wilson}, Geom. Dedicata 26, 157-170 (1988; Zbl 0643.51015)].