Error bounds for the method of good lattice points

Abstract

New error bounds are obtained for the method of good lattice points for multidimensional quadrature, when <italic>m</italic> , the number of quadrature points, is prime. One of these bounds reduces the constant in Niederreiter’s asymptotic error bound, if the dimension exceeds 2. Together they give very much smaller numerical bounds for all values of <italic>m</italic> .