A note on strong blocking sets and higgledy-piggledy sets of lines

This paper studies { strong blocking sets} in the N-dimensional finite projective space PG(N,q). We first show that certain unions of blocking sets cannot form strong blocking sets, which leads to a new lower bound on the size of a strong blocking set in PG(N,q). Our second main result shows that, for q>2/ln(2)(N+1), there exists a subset of $2N-2$ lines of a Desarguesian line spread in PG(N,q), N odd, in { higgledy-piggledy arrangement}; thus giving rise to a strong blocking set of size $(2N-2)(q+1)$.