The maximum size of a partial spread in \(H(5,q^{2})\) is \(q^{3}+1\)
A spread of a polar space is a set of mutually skew generators that partition the polar space. According to \textit{J. A. Thas} the finite Hermitian polar space \(H(d,q^2)\), \(d\) odd, does not possess any spread [Ann. Discrete Math. 52, 529--544 (1992; Zbl 0767.51004)], and for \(d=5\) an upper bound for the size of a partial spread is given by \(q^4\) (D. Luyckx). The authors are able to reduce this bound down to \(q^3+1\). Moreover, they improve the lower bound \(q+1\) for the number of planes that a partial spread of \(H (5,q^2)\), \(q\geq7\), contains to \(2q+3\).
scientific article; zbMATH DE number 5151551
scientific article