A spectrum result on maximal partial ovoids of the generalized quadrangle Q(4,q), q even

Abstract

AbstractThis article presents a spectrum result on maximal partial ovoids of the generalized quadrangle Q(4,q), q even. We prove that for every integer k in an interval of, roughly, size [q2/10,9q2/10], there exists a maximal partial ovoid of size k on Q(4,q), q even. Since the generalized quadrangle W(q), q even, defined by a symplectic polarity of PG(3,q) is isomorphic to the generalized quadrangle Q(4,q), q even, the same result is obtained for maximal partial ovoids of W(q), q even. As equivalent results, the same spectrum result is obtained for minimal blocking sets with respect to planes of PG(3,q), q even, and for maximal partial 1-systems of lines on the Klein quadric Q+(5,q), q even