We construct two-weight sets in PG\((3n-1,q)\), \(n\geq2\) with the same weights as those that would arise from the blow-up of a maximal \(q\)-arc in PG\((2,q^n)\). The construction is of particular interest when \(q\) is odd, as it is well known that no maximal arcs in PG\((2,q^n)\) exist in that case.

Mathematics Subject Classifications: 51E20, 05B25

Keywords: Projective two-weight set, maximal arc