Exterior sets of hyperbolic quadrics (Q1590259)

An exterior set of a hyperbolic quadric \(Q=Q^+ (2n-1,q)\) in \(PG(2n-1,q)\) is a point set \(X\) for which no line joining two distinct elements of \(X\) intersects \(Q\). It is easy to see that \(|X|\leq (q^n-1)/(q-1)\), and all exterior sets meeting this bound were classified by \textit{J. A. Thas} in 1991 [J. Comb. Theory, Ser. A 56, No. 2, 303-308 (1991; Zbl 0721.51009)]; with one exception in \(PG(5,2)\), one always has the case of dimension \(d=3\). The author obtains recursively stronger upper bounds than the obvious one, based on a detailed investigation of the case of dimension 5.