The maximum complete (k, n)‎-arcs in the projective plane PG(2, 4)‎ by geometric method

الملخص EN

A (k, n)-arc A in a finite projective plane PG(2,q) over Galois field GF(q), q = pⁿ for same prime number p and some integer n≥2, is a set of k p oints, no n + 1 of which are collinear.

A (k, n)-arc is complete if it is not contained in a(k+1,n)-arc.

In this paper, the maximum complete (k,n)-arcs, n = 2,3 in PG(2,4) can be constructed from the equation of the conic.