On minimum size blocking sets of external lines to a quadric in \(\text{PG}(3, q)\)
Let \(\mathcal Q\) be a non-degenerate quadric in \(\text{PG}(3, q)\), \(q\geq9\). The authors characterize all minimum size sets \(B\) such that each line external to \(\mathcal Q\) meets \(B\). More precisely, they prove that if \(Q\) is a hyperbolic quadric, then \(| B| =q^2-q\) and \(B=\pi\setminus\mathcal Q\), where \(\pi\) is a plane tangent to \(Q\); if \(Q\) is an elliptic quadric, then \(| B| =q^2\) and \(B=\pi\setminus\mathcal Q\), where \(\pi\) is a plane secant to \(Q\); if \(Q\) is a quadratic cone, then \(| B| =q^2-q\) and \(B=\pi\setminus\mathcal Q\), where \(\pi\) is a plane sharing two distinct lines with \(Q\). Part of such a characterization was given in a submitted paper by P. Biondi and P. M. Lo Re (On blocking sets of external lines to a hyperbolic quadric in \(\text{PG}(3,q)\), \(q\) even).
scientific article; zbMATH DE number 5152749