Vol. 3, No. 1, 2006

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Small maximal partial ovoids of $H(3,q^2)$

Klaus Metsch

Vol. 3 (2006), No. 1, 1–11
Abstract

The trivial lower bound for the size of a maximal partial ovoid of H(3,q2) is q2 + 1. Ebert showed that this bound can be attained if and only if q is even. In the present paper it is shown that a maximal partial ovoid of H(3,q2), q odd, has at least q2 + 1 + 4 9q points (previously, only q2 + 3 was known). It is also shown that a maximal partial spread of H(3,q2), q even, has size q2 + 1 or size at least q2 + 1 + 4 9q.

Keywords
ovoid, polar space, Hermitian variety
Mathematical Subject Classification 2000
Primary: 05B25, 51E12, 51E20
Milestones
Received: 14 March 2006
Accepted: 8 May 2006
Authors
Klaus Metsch