Maximal partial spreads of T-2(O) and T-3(O)

Assuming a partial spread of Full-size image (<1 K) or Full-size image (<1 K), with deficiency δ, 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 Full-size image (<1 K) 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 Full-size image (<1 K), and, furthermore, this result is sharp since partial spreads with deficiency δ=q are constructed.