Bounds for Arcs of Arbitrary Degree in Finite Desarguesian Planes

摘要

This paper examines subsets with at most n points on a line in the projective plane . A lower bound for the size of complete -arcs is established and shown to be a generalisation of a classical result by Barlotti. A sufficient condition ensuring that the trisecants to a complete (k, 3)-arc form a blocking set in the dual plane is provided. Finally, combinatorial arguments are used to show that, for , plane (k, 3)-arcs satisfying a prescribed incidence condition do not attain the best known upper bound.