Small maximal partial spreads in classical finite polar spaces

Abstract

Abstract We prove lower bounds on the size of small maximal partial spreads in Q +(4n + 1, q), W(2n + 1, q), and H(2n + 1, q 2). This research on the size of smallest maximal partial spreads in classical finite polar spaces is part of a detailed study on small and large maximal partial ovoids and spreads in classical finite polar spaces, performed in [De Beule, Klein, Metsch, Storme, Des. Codes Cryptogr 47: 21–34, 2008, De Beule, Klein, Metsch, Storme, European J. Combin 29: 1280–1297, 2008].