The largest size of the arc of degree three in a projective plane of order sixteen

An (n;3)-arc K in projective plane PG(2,q) of size n and degree three is a set of n points satisfies that every line meets it in less than or equal three points, also it is complete if it is not contained in (n+1;3)-arc. The goals of this paper are to construct the projectively inequivalent (n;3)-arcs in PG(2,16), determined the largest complete arc in PG(2,16), the stabilizer group of these arcs and we have identified the group with which its isomorph.