A new upper bound for the largest complete (k, n)-arc in PG(2, 71)

In this current work, we are presenting a new upper bound for some m n (2, 71). Generally, In the projective plane in the two dimensional projective geometry of order q (briefly denoted by PG(2, q )) over a selected field F q of a q number of components, a ( k, n )-arc can be defined as the set K of k number of points having mostly n number of points on any selected line of the plane. Therefore, this work can be done after determining what is k such that K becomes complete, as well as, these K values are not included in a ( k +1, n )-arc. Particularly, finding a value that represents the largest existent value k for a complete K , that can be written as m n (2, q ). In this current projective plane, the blocking set represents the complement of a ( k, n )-arc K in the two dimensional projective geometry of order q with s = q + 1 - n .