A class of ((p n−p m)(p n−1), p n−p m)-arcs in PG(2, p n)

A (k, d)-arc in PG(2, q) is a set of k points such that some d, but no d+1, of them are collinear. An outstanding problem is to find the maximum value of k for which a (k, d)-arc exists. A construction is given for a class of (k, pⁿ–p^m)-arcs in PG(2, pⁿ). These arcs constitute a lower bound on the maximum possible value of k, and a subset of them is shown to be optimal.