Blocking sets and partial spreads in finite projective spaces

Abstract

A t-blocking set in the finite projective space PG(d, q) with d≥t+1 is a set $\mathfrak{B}$ of points such that any (d−t)-dimensional subspace is incident with a point of $\mathfrak{B}$ and no t-dimensional subspace is contained in $\mathfrak{B}$. It is shown that |$\mathfrak{B}$|≥q ^t+...+1+q ^t−1√q and the examples of minimal cardinality are characterized. Using this result it is possible to prove upper and lower bounds for the cardinality of partial t-spreads in PG(d, q). Finally, examples of blocking sets and maximal partial spreads are given.