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 $\mathscr{K}$ 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 $\mathscr{K}$ 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 $\mathscr{K}$ , 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 $\mathscr{K}$ in the two dimensional projective geometry of order q with s = q + 1 - n.