Blocking subspaces by lines in \(PG(n,q)\) (Q558245)

This paper studies the cardinality of a smallest set \(T\) of \(t\)-subspaces of the finite projective space PG\((n,q)\) such that every \(s\)-subspace is incident with at least one element of \(T\), where \(0\leq t\leq s\leq n\). Solution of this problem is known only for very few families of triples \((s,t,n)\). When the answer is known, the corresponding blocking configurations usually are partitions of a subspace PG\((n,q)\) by subspaces of dimension \(t\). One of the exceptions is the solution in the case \(t=1\) and \(n=2s\). In this paper is given the solution of the case when \(t=1\) and \(2s<n\leq 3s-3\) and \(q\) is sufficiently large.