The Construction of Complete (k,n)-arcs in 3-Dimensional Projective Space Over Galois Field GF(4)

In this work, we construct the projectively distinct (k,n)-arcs in PG(3,4) over Galois field GF(4), where k ≥ 5, and we found that the complete (k,n)-arcs, where 3 ≤ n ≤ 21, moreover we prove geometrically that the maximum complete (k,n)-arc in PG(3,4) is (85,21)-arc.A(k,n)-arcs is a set of k points no n+1 of which are collinear .A(k,n)-arcs is complete if it is not contained in a (k+1,n)-arcs.