Abstract :
We consider the problem of the existence of covering sets of spreads in PG(3,q). This is connected with the problem of extending the linear space of points and lines in the projective 3-space PG(3,q) to a projective plane of order q(q+1). The concept of an ℓ-local covering set is introduced and a particular type, which is called special, is defined. We show, using a computer search, that there is no covering set in PG(3,4) which involves a special local covering set.
