Known Ovoids

There are three types of quadrics, parabolic, hyperbolic and elliptic giving the spaces Ω(2n+1, q),Ω+(2n, q),Ω−(2n, q), respectively, and we have seen that ovoids exist in Ω+(8, q)-spaces and Ω(7, q)-spaces. However, there are a variety of ovoids in the Klein quadric, which we shall list below. Furthermore ovoids in PG(3, q) may be defined without associated quadrics.