Construction and Comparison of High-Dimensional Sobol' Generators

Sobol' sequence generators are actively used in financial applications. In this paper, we explore the effect of the uniformity properties A and A' on the generator performance in high dimensional problems. It is shown that these properties provide an additional guarantee of uniformity for high-dimensional problems even at a small number of sampled points. By imposing additional uniformity properties on low dimensional projections of the sequence in addition to the uniformity properties of the d-dimensional sequence itself the efficiency of the Sobol' sequence can be increased. The SobolSeq16384 generator which satisfies additional uniformity properties (Property A for all 16384 dimensions and Property A' for adjacent dimensions) is constructed. A comparison of known Sobol' sequence generators for a set of tests shows that for majority of tests the SobolSeq16384 generator performs better than other generators.