Blocking sets and partial spreads in finite projective spaces

A t-blocking set in the finite projective space PG(d, q) with dt+1 is a set of points such that any (d–t)-dimensional subspace is incident with a point of and no t-dimensional subspace is contained in . It is shown that | |q ^t +...+1+q ^t–1q 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.