Irregular weighting of 1-designs

Assign positive integer weights to the edges of a hypergraph in such a way that summing up the weights of the edges through a point yields distinct integers for different points. In this note we give a lower bound for the maximal edgeweight in case the hypergraph is uniform and regular, i.e. it is a 1-design. If the hypergraph is the dual of a 2-(v,k,¿) design then this bound specializes to . In particular for a projective plane this number is at least .