Let \(q\) be the order of a finite projective plane \(\Pi\) and \(2\leq n\leq q.\) A maximal \(\{q(n-1)+n;n\}\)-arc is a subset of \(q(n-1)+n\) points in \(\Pi\) that meets every line in \(0\) or \(n\) points. The authors present the results of computer searches for such arcs in all the known planes of order 16 with \(n=4.\) They also classify pairs of disjoint such arcs inside the list of arcs obtained. Finally, the authors give some results on resolvable 2-\((52,4,1)\) designs associated with maximal arcs as above.