On the number of directions determined by a point set in AG\((2,p)\) (Q1808796)

It is known that a \(p\)-element point set in \(\text{AG}(2,p)\), different from a line determines at least \((p+3)/2\) directions. The author looks for sets determining more than \((p+3)/2\) directions. He proves that apart from two examples, no set determines \((p+5)/2\) directions. He also gives an infinite series of examples determining \(7p/9\) directions proving some results on the graph of monomials. Finally, he formulates a conjecture: no point set can determine \(N\) directions with \((p+3)/2<N<2p/3\).