Saturated configurations of points in projective Galois spaces (Q1103189)

A set K of k points in PG(r,q) is said to be \(\rho\)-saturated for some integer \(\rho\) :\(1\leq \rho \leq r-1,\) if, for any point \(x\in PG(r,q)\), there exist \(\rho +1\) linearly independent points \(x_ 0,...,x_{\rho}\in K\) such that \(x\in J(x_ 0,...,x_{\rho})\), where the symbol \(J(a_ 0,...,a_ n)\) denotes the join of the points \(a_ 0,...,a_ n\). The author studies such sets and gives estimates for the smallest possible value of k, when r,q,\(\rho\) are given.