On multiple nuclei and a conjecture of Lunelli and Sce
A point \(p \not \in S\) is called a \(t\)-fold nucleus of a point set \(S\) contained in an affine plane \(AG (2,q)\), if every line through \(p\) intersects \(S\) at least \(t\) points. The author obtains an upper bound on the number of points which is then applied to obtain an improved lower bound of \((t + 1)q - 1\) on the cardinality of a \(t\)-fold blocking set of \(AG (2,q)\), provided that \(t\) and \(q\) are relatively prime. As a further application, the truth of the Lunelli-Sce conjecture on maximal \((k,n)\)- arcs is established for affine planes.
scientific article; zbMATH DE number 617009
scientific article