Small maximal partial t-spreads in PG(2t+1,q)

A maximal partial t-spread in a projective space is a set of t-spaces which are pairwise disjoint, such that this set is non-extendable with respect to this condition. In this article we prove a lower bound on the size of a maximal partial t-spread in the projective space PG(2t+1,q) by using the method due to Glynn for t=1. We also find a lower bound on the size of a maximal partial t-spread containing a small blocking set.