Bounds for arcs of arbitrary degree in finite desarguesian planes

This paper examines subsets with at most n points on a line in the projective plane p q = PG(2, q). A lower bound for the size of complete (k, n)-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 B in the dual plane p* q is provided. Finally, combinatorial arguments are used to show that, for q = 17, plane (k, 3)-arcs satisfying a prescribed incidence condition do not attain the best known upper bound.