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, 3 q 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 Rößing 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.