... few results on the linearity of small minimal k -blocking sets andon the size of small k -blocking sets t hat will be used thro ug hout this paper. The first of the following theorems of Sz˝onyi and ... for the size of the intersection that areobtained in this statement, can occur (see [7]). The bound on the characteristic of the field appearing in Main Theorem 2 arises from this theorem.Theorem ... prove the linearity of small minimal 1 -blocking sets inPG(n, pt), which reproofs the mentioned statements of Storme and Weiner in the casest = 2, 3. The techniques developed in [6] to show the...