Description
Abstract:
A double blocking set in a finite projective plane is a set of points which meets every line in at least two points. A trivial example for a double blocking set is the union of three non-concurrent lines (that is, a triangle), which is of size 3q if the order of the plane is q.
It is particularly interesting to find double blocking sets in PG(2,q) (the classical projective plane coordinatized by the finite field of q elements) of size less than 3q when q is a prime, in which case the only example known up to 2019 was one of size 38 = 3q-1 in PG(2,13) found by Braun, Kohnert and Wassermann (2005). In [B. Csajbók, T. Héger: Double blocking sets of size 3q-1 in PG(2,q), Eur. J. Comb., 2019] we studied in detail a particular construction idea which led to examples of double blocking sets of size 3q-1 in PG(2,q) for q=13, 16, 19, 25, 27, 31, 37 and 43 (found by computer search) and to the resolution of two minor conjectures of R. Hill from 1984. In the talk we will discuss these results.