Maximal partial spreads of T_2(O) and T_3(O)

摘要

Assuming a partial spread of T_2(O) or T_3(O), with deficiency , is maximal and using results on minihypers, which are closely related to blocking sets in PG(2,q), we obtain lower bounds for δ. If q is even, using extendability of arcs in PG(2,q), we prove that a maximal partial spread of T_2(O) which does not cover (∞) does not exist if δ ≤ q-1. This improves a theorem of Tallini (Proceedings of the First International Conference on Blocking Sets (Giessen, 1989) 201 (1991) 141) for T_2(O) approx.= Q(4,q), and, furthermore, this result is sharp since partial spreads with deficiency δ=q are constructed.