Blocking sets of certain line sets related to a hyperbolic quadric in \(\mathrm{PG}(3, q)\) (Q2334547)

A blocking set with respect to a set of lines is a subset of the point set such that each line contains at least one point of the blocking set. Let \(E\) be the sets of lines external to a hyperbolic quadric in \(\mathrm{PG}(3,q)\), \(T\) be the sets of lines tangent to a hyperbolic quadric in \(\mathrm{PG}(3,q)\), and \(S\) be the sets of lines secant to a hyperbolic quadric in \(\mathrm{PG}(3,q)\). The authors characterize the minimum size blocking sets of \(\mathrm{PG}(3,q)\) with respect to the line sets \(S\), \(T \cup S\), and \(E \cup S\).