Subgroup-based Rank-1 Lattice Quasi-Monte Carlo

Quasi-Monte Carlo (QMC) is an essential tool for integral approximation, Bayesian inference, and sampling for simulation in science, etc. In the QMC area, the rank-1 lattice is important due to its simple operation, and nice property for point set construction. However, the construction of the generating vector of the rank-1 lattice is usually time-consuming through an exhaustive computer search. To address this issue, we propose a simple closed-form rank-1 lattice construction method based on group theory. Our method reduces the number of distinct pairwise distance values to generate a more regular lattice.