On small {;k; q};-arcs in planes of order q2

In this paper we examine some properties of complete {;k; q};-arcs in projective planes of order q². In particular, we derive a lower bound for k, and we exhibit a family of arcs having low values of k which exist in every such plane having a Baer subplane. In addition we resolve the existence problem for complete {;k; 3};-arcs in PG(2, 9).