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.