New \((k;r)\)-arcs in the projective plane of order thirteen (Q1882439)

A \((k,r)\)-arc in PG(\(2,q\)) is a \(k\)-subset \(A\) of points that at most \(r\) points in \(A\) are collinear. With a computer search as well as some theoretical reasoning, the authors construct \((35,4)\), \((48,5)\), \((63,6)\) and \((117,10)\)-arcs in PG(\(2,13\)). Finally, the nonexistence of a \((40,4)\)-arc \(A\) in PG(\(2,13\)) is established, provided that no line meets \(l\) in precisely \(2\) points.