In a geometry the notion of
blocking set ordinarily refers to a set of points meeting every line. (For projective
planes convention requires in addition that the blocking set not contain all the points
of any one line.) In this paper we obtain lower bounds for the size of a blocking set
for projective planes and inversive planes, which are equal to or improvements on the
best previously known bounds. If the notion of blocking set is generalized to families
of disjoint subspaces rather than sets of points, then (partial) spreads are
included, and we obtain a lower bound for the size of a maximum partial
spread of m-spaces in projective (2m + 1)-space. The technique is that of
Glynn, counting various sets of intersecting subspaces in two ways to obtain
inequalities.
