The conventional Monte Carlo approach to integration and simulation is a useful alternative to analytic or quadrature methods. It has been recognized through theory and practice that a variety of uniformly distributed sequences provide more accurate results than a purely pseudorandom sequence....

Relations between Monte Carlo and quasi-Monte Carlo methods are analysed from both theoretical and practical points of view with special emphasis on high-dimensional integration.

It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]....