Minimal blocking sets of size q2+2 of Q(4,q), q an odd prime, do not exist

It is known that every blocking set of Q(4,q), q>2 even, with less than points contains an ovoid, and hence Q(4,q) has no minimal blocking set with . In contrast to this, it is even not known whether or not Q(4,q), q odd, has minimal blocking sets of size q2+2. In this paper, the non-existence of a minimal blocking set of size q2+2 of Q(4,q), q an odd prime, is shown. Strong geometrical information is obtained using an algebraic description of W(3,q). Geometrical and combinatorial arguments complete the proof.