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Let $\Pi_q$ be an arbitrary finite projective plane of order $q$. A subset$S$ of its points is called saturating if any point outside $S$ is collinearwith a pair of points from $S$. Applying probabilistic tools we improve theupper bound on the smallest possible size of the saturating set to$\lceil\sqrt{3q\ln{q}}\rceil+ \lceil(\sqrt{q}+1)/2\rceil$. The same result ispresented using an algorithmic approach as well, which points out theconnection with the transversal number of uniform multiple intersectinghypergraphs.

Saturating sets in projective planes and hypergraph covers