A new geometric method for constructing complete (k, n)-arcs in PG(3,11)

In this work, we construct a complete (k,n)-arcs in the projective space over Galois field GF(11), we construct the complete (k,n)-arcs by taking the union of some (k,n)-arcs, where 3 ≤ n ≤ 10, also, we construct the complete (k,n + 1)-arcs from the complete (k,n)-arcs, where 10 ≤ n ≤ 133 , by using computer program A,B we added some points of index zero, and found all the complete (k,n)-arcs in PG(3,11), where 3 ≤ n ≤ 133. Moreover, we prove geometrically that the maximum complete (k,n)-arc in PG(3,11) is (1464,133)-arc.