On \(k\)-arcs covering a line in finite projective planes.
Consider a line in a \(\text{PG}(2,q)\). A \(k\)-arc covers the line, if every point of the line lies on a secant of the arc. The authors show that there exist covering \(k\)-arcs with \(k\) approximately \(2\sqrt {\mathstrut q}\), prove \(k \geq (1+\sqrt {8q+9})/2\) and establish when the equality holds. They also connect the notion of covering arcs to the notion of perfect hash families.
scientific article; zbMATH DE number 1600990