New families of ovoids in \(O\) \(+_ 8\) (Q1101957)

An ovoid in the 8-dimensional orthogonal geometry \(O\) \(+_ 8(q)\) (q a prime-power) may be thought of as a set of q \(3+1\) points (isotropic 1- spaces) no two of which are orthogonal. The authors construct four infinite families of ovoids in \(O\) \(+_ 8(p)\), and determine their automorphism groups. They show that four previously known ovoids, including two found recently, are members of the families.