On the size of a maximal partial spread

We show that a maximal partial spread inPG(3,q) is either a spread or has at most q2 + 1 - Ö{2q}q2+1-2qlines. This implies that it is not possible to cover all points but the points of a Baer-subspace by lines

Partial ovoids and partial spreads in Hermitian polar spaces

We present improved lower bounds on the sizes of small maximal partial ovoids in the classical hermitian polar spaces, and improved upper bounds on the sizes of large maximal partial spreads in the classical hermitian polar spaces. Of particular importance is the presented upper bound on the size of a maximal partial spread of H(3,q(2)). For q = 2,3, the presented upper bound is sharp. For q = 3, our results confirm via theoretical arguments properties, deduced by computer searches performed by Ebert and Hirschfeld, for the largest partial spreads of H(3,9). An overview of the status regarding these results is given in two summarizing tables. The similar results for the classical symplectic and orthogonal polar spaces are presented in De Beule et al. [8]