The largest 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 $ 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.