  We examine sets of lines in PG(d,F) meeting each hyperplane in a generator
set of points. We prove that such a set has to contain at least 1.5d lines if
the field F has more than 1.5d elements, and at least 2d-1 lines if the field F
is algebraically closed. We show that suitable 2d-1 lines constitute such a set
(if |F| > or = 2d-1), proving that the lower bound is tight over algebraically
closed fields. At last, we will see that the strong (s,A) subspace designs
constructed by Guruswami and Kopparty have better (smaller) parameter A than
one would think at first sight.
