  In a recent paper by the authors, it is shown that there exists a quasi-Monte
Carlo (QMC) rule which achieves the best possible rate of convergence for
numerical integration in a reproducing kernel Hilbert space consisting of
smooth functions. In this paper we provide an explicit construction of such an
optimal order QMC rule. Our approach is to exploit both the decay and the
sparsity of the Walsh coefficients of the reproducing kernel simultaneously.
This can be done by applying digit interlacing composition due to Dick to
digital nets with large minimum Hamming and Niederreiter-Rosenbloom-Tsfasman
metrics due to Chen and Skriganov. To our best knowledge, our construction
gives the first QMC rule which achieves the best possible convergence in this
function space.
