Construction of complete and maximal (k, n) arcs in the projective plane pg (2, 7 )

Abstract

The purpose of this paper is to study the construction of complete and maximal (k , n)- arcs in the projective plane PG (2 , 7) , n = 2 , 3, ...,8 . A (k, n) –arc K in a projective plane is a set of K points such that no n + 1 of which are collinear. A (k, n) –arc is complete if it is not contained in a (k + 1, n) – arc. A (k, n) – arc is a maximal if and only if every line in PG ( 2 , P ) is a O – secant , or n – secant , which represented as ( k , 2 ) – arc and ( k , 8) – arc