A spectrum result on minimal blocking sets with respect to the planes of PG(3,q), q odd

This article presents a spectrum result on minimal blocking sets with respect to the planes of PG(3, q), q odd. We prove that for every integer k in an interval of, roughly, size [q (2)/4, 3q (2)/4], there exists such a minimal blocking set of size k in PG(3, q), q odd. A similar result on the spectrum of minimal blocking sets with respect to the planes of PG(3, q), q even, was presented in Roing and Storme (Eur J Combin 31:349-361, 2010). Since minimal blocking sets with respect to the planes in PG(3, q) are tangency sets, they define maximal partial 1-systems on the Klein quadric Q (+)(5, q), so we get the same spectrum result for maximal partial 1-systems of lines on the Klein quadric Q (+)(5, q), q odd