Maximal partial ovoids and maximal partial spreads in hermitian generalized quadrangles

Maximal partial ovoids and maximal partial spreads of the hermitian generalized quadrangles H(3, q(2)) and H(4, q(2)) are studied in great detail. We present improved lower bounds on the size of maximal partial ovoids and maximal partial spreads in the hermitian quadrangle H(4, q(2)). We also construct in H(3, q(2)), q = 2(2h+1), h >= 1, maximal partial spreads of size smaller than the size q(2) + 1 presently known. As a final result, we present a discrete spectrum result for the deficiencies of maximal partial spreads of H(4, q(2)) of small positive deficiency S. (C) 2007 Wiley Periodicals, Inc.