Minimal Blocking Sets Arising from Joining Some of the Smallest Singer Orbits

A blocking set in a finite projective plane is defined as a set of points which meets every line. Since lines are the smallest blocking sets, a blocking set containing a line is called trivial. A blocking set is minimal when no proper subset of it is a blocking set. In the literature, there are plenty of constructions for minimal blocking sets by considering suitable Singer orbits of points. The most studied minimal blocking sets are those consisting of a single Singer orbit and not much seems to be known about the general case of those consisting of unions of several small orbits. The question arises whether a generalization would be possible when the size of Singer orbits is the smallest. In this paper, we propose a different method for constructing minimal blocking sets using the smallest Singer orbits, and we provide minimal blocking sets by joining some of them.