Blocking Sets of Size qt+qt−1+1

We prove that in the desarguesian plane PG(2, qt) (t>4) there are at least three inequivalent blocking sets of size qt+qt−1+1. The first one has q+1 Rédei lines, the second one has exactly one Rédei line, and the third one is not of Rédei type. For GF(q) the largest subfield of GF(qt), our results disprove a conjecture quoted by A. Blokhuis (1998, in “Galois Geometry and Generalized Polygons,” Gent).