A spectrum result on maximal partial ovoids of the generalized quadrangle , even

This 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 [ q 2 / 10 , 9 q 2 / 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 P G ( 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 P G ( 3 , q ) , q even, and for maximal partial 1-systems of lines on the Klein quadric Q + ( 5 , q ) , q even.