An explicit construction of point sets with large minimum Dick weight

Abstract

The Dick weight is a generalization of the Hamming weight and the Niederreiter–Rosenbloom–Tsfasman (NRT) weight, defined on Fps×n. A point set with large value of minimum Dick weight gives a quadrature rule with small error in quasi-Monte Carlo integration. In this paper we explicitly construct point sets P⊂Fps×n with large minimum Dick weight using Niederreiter–Xing sequences and Dick’s interleaving construction. These point sets are also examples of low-WAFOM point sets.