Multiple blocking sets in PG(n,q), n>=3.

This article discusses minimal s-fold blocking sets B in PG (n, q), q = ph, p prime, q > 661, n > 3, of size |B| > sq + cp q2/3 - (s - 1) (s - 2)/2 (s > min (cp q1/6, q1/4/2)). It is shown that these s-fold blocking sets contain the disjoint union of a collection of s lines and/or Baer subplanes. To obtain these results, we extend results of Blokhuis–Storme–Szönyi on s-fold blocking sets in PG(2, q) to s-fold blocking sets having points to which a multiplicity is given. Then the results in PG(n, q), n ≥ 3, are obtained using projection arguments. The results of this article also improve results of Hamada and Helleseth on codes meeting the Griesmer bound.