Blocking sets of tangent and external lines to a hyperbolic quadric in PG(3,q)

Let H be a hyperbolic quadric in PG(3,q), where q is a prime power. Let E (respectively, T) denote the set of all lines of PG(3,q) which are external (respectively, tangent) to H. We characterize the minimum size blocking sets in PG(3,q), q≠2, with respect to the line set E∪T. We also give an alternate proof characterizing the minimum size blocking sets in PG(3,q) with respect to the line set E for all odd q.