On \(q^ 2/4\)-sets of type \((0,q/4,q/2)\) in projective planes of order \(q\equiv 0\pmod 4\)
Let \(H\) be a hyperoval in a finite projective plane \(\Pi\) of order \(q\); a triple of points \(x,y,z\) not in \(H\) is said to be regular if there is no point \(p\) such that all three lines \(px\), \(py\) and \(pz\) are exterior lines of \(H\). Regular triples of points were introduced by the first author (``Regular triples with respect to a hyperoval'', Ars Comb., to appear) who proved that they lead to sets of cardinality \(q^ 2/4\) and type \((0, q/4, q/2)\) in \(\Pi\); in particular, \(q\) has to be a multiple of 4. In the paper under review, the authors study such sets in general and provide two different classes of examples in \(\text{PG} (2,2^ h)\) for all \(h \geq 3\).
scientific article; zbMATH DE number 599968
scientific article