ARCS in the Projective Plane Over Some Finite Fields

The investigation of arcs in finite projective planes focuses on analyzing their sizes, structural characteristics, and their connections with other geometric configurations. Arcs can be classified according to several features, including their cardinality and degree. This work examines arcs in the finite projective spaces PG(2,q) for q=25,27. The study is based on the orbits obtained from the action of the projective linear groups PGL(3,25) and PGL(3,27) on PG(2,25) and PG(2,27), respectively. Furthermore, each obtained arc is extended according to its degree until a complete arc is achieved.