A spectrum result on maximal partial ovoids of thegeneralized quadrangle Q(4, q) , q odd

摘要

In this article, we prove a spectrum result on maximal partialovoids of the generalized quadrangle Q(4, q), q odd, i.e. for every integer kin the interval [a, b], where a≈3/5sq~2andb≈9/10q~2, there exists a maximalpartial ovoid of Q(4, q), q odd, of size k. Since the generalized quadrangleW(q) defined by a symplectic polarity of PG(3,is isomorphic to the dualof the generalized quadrangle Q(4, q), the same result is obtained for maximalpartial spreads of W (q), q odd. This article concludes a series of articles onspectrum results on maximal partial ovoids of Q(4, q), on spectrum resultson maximal partial spreads of W (q) , on spectrum results on maximal partial1-systems of Q~+ (5, q),and on spectrum results minimal blocking sets withrespect to the planes of PG(3, q). We conclude this article with the tablessummarizing the results.