Classification of degree three arcs in PG(2,19) up to stabilizer groups

Abstract

An -arc  in projective plane  of size  and degree three is a set of n points such that every line in the plane meet it in less than or equal three points, also the arc  is complete if it is not contained in -arc. In this paper, the classification of degree three arcs in  is introduced in details according to their stabilizer groups. The motivation for working in the projective plane of order  is twofold. First, the size of the largest -arc is not known. Second, the number of -arcs is significantly higher in the projective plane of order  than it is in the projective plane of order  for , giving a large number of -arcs for the study.