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

Document Type : Research Paper


Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq


 An $(n;3)$-arc in projective plane $PG(2,q)$ of size n and degree three is a set of n points such that no four of them collinear but some three of them are collinear.An $(n;r)$-arc is said to be complete if it is not contained in $(n+1;r)$-arc.  The aim of this paper is to construct the projectively distinct$(n;3)$-arcs in $PG(2,16)$, determined the smallest complete arc in $PG(2,16)$ then the stabilizer group of these arcs are established and we have identified the group with which it's isomorphic.