This paper by Paul Bratley and Bennett L. Fox compares the accuracy and speed of low-discrepancy sequence generators, specifically Sobol' and Faure, which are useful for multidimensional integration and global optimization. The authors discuss their implementation of the Sobol' generator and compare it in detail with the Faure generator, which Fox previously found to be more efficient than Halton's technique. The paper provides an informal description of the necessary computations for generating quasirandom sequences using Sobol's method, including the use of direction numbers derived from primitive polynomials. It also covers the choice of initial values, computational complexity, and favorable values for the sequence. The authors test the generators using a specific integral and provide timing results, showing that the Faure and Sobol' generators are roughly matched in accuracy, with the Sobol' generator being significantly faster when implemented with a nonstandard exclusive-or function. The paper concludes with recommendations for the use of these generators based on the experimental results.This paper by Paul Bratley and Bennett L. Fox compares the accuracy and speed of low-discrepancy sequence generators, specifically Sobol' and Faure, which are useful for multidimensional integration and global optimization. The authors discuss their implementation of the Sobol' generator and compare it in detail with the Faure generator, which Fox previously found to be more efficient than Halton's technique. The paper provides an informal description of the necessary computations for generating quasirandom sequences using Sobol's method, including the use of direction numbers derived from primitive polynomials. It also covers the choice of initial values, computational complexity, and favorable values for the sequence. The authors test the generators using a specific integral and provide timing results, showing that the Faure and Sobol' generators are roughly matched in accuracy, with the Sobol' generator being significantly faster when implemented with a nonstandard exclusive-or function. The paper concludes with recommendations for the use of these generators based on the experimental results.