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

作者：Roessing C^*; Storme L

来源：European Journal of Combinatorics, 2010, 31(1): 349-361.

DOI：10.1016/j.ejc.2009.01.003

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 vertical bar q(2)/10, 9q(2)/10 vertical bar, 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.

• 出版日期2010-1