On maximal partial spreads of H(2n+1,q2)H(2n+1,q2)

A lower bound for the size of a maximal partial spread of H(2n+1,q2)H(2n+1,q2) is given. For H(2n+1,q2)H(2n+1,q2) in general, and for H(5,q2)H(5,q2) in particular, new upper bounds for this size are also obtained. In [A. Aguglia, A. Cossidente, G.L. Ebert, Complete spans on Hermitian varieties, in: Proceedings of the Conference on Finite Geometries (Oberwolfach, 2001), vol. 29, 2003, pp. 7–15.], maximal partial spreads of H(3,q2)H(3,q2) and H(5,q2)H(5,q2) have been constructed from spreads of W3(q)W3(q) and W5(q)W5(q), respectively; the construction for H(5,q2)H(5,q2) will be generalized to H(4n+1,q2)H(4n+1,q2), n⩾1n⩾1, thus yielding examples of maximal partial spreads of H(4n+1,q2)H(4n+1,q2) for all n⩾1n⩾1.