Efficient scramble for quasi-random numbers in Monte Carlo computations

Because in Monte Carlo computations the generation of random numbers is the most important factor in the accuracy of computation, we assume that the maximum uniformity in the interval (0, 1) is used in this calculation. In this paper, we first provide a short review of Halton and Faure sequences for generating quasi-random numbers, and then, we investigate the improvement of scrambles of Faure sequence in Monte Carlo Computation for stochastic integrals. In fact, using scrambled quasi-random numbers in Monte Carlo calculations, we show that this change in the method of generating quasi-random numbers yields significant results. Additionally, we show that partitioning the random number generators improves Monte Carlo computations by reducing errors.