Maximal partial line spreads of non-singular quadrics

Abstract

For n ≥ 9, we construct maximal partial line spreads for non-singular quadrics of P G(n, q) for every size between approximately (cn + d)(q n−3 + q n−5 ) log 2q and q n−2 , for some small constants c and d. These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gács and Szőnyi. These results also extend spectrum results on maximal partial line spreads in the finite generalized quadrangles W 3 (q) and Q(4, q) by Pepe, Rößing and Storme.

Constant Rank-Distance Sets of Hermitian Matrices and Partial Spreads in Hermitian Polar Spaces

“…We now turn our attention to the question of the existence of an interval of integers such that, for each integer contained, there exists a maximal partial spread of that size. This question has received attention for the case of PG(3, q) ( [19]), W (3, q) and Q(4, q) ( [30], [29], [31]). We now construct maximal partial spreads in H(3, q 2 ) for a range of sizes.…”