On saturating sets in projective spaces

Minimal saturating sets in projective spaces PG(n,q) are considered. Estimates and exact values of some extremal parameters are given. In particular the greatest cardinality of a minimal 1-saturating set has been determined. A concept of saturating density is introduced. It allows to obtain new lower bounds for the smallest minimal saturating sets. A number of exhaustive results for small q are obtained. Many new small 1-saturating sets in PG(2,q), q⩽587, are constructed by computer.