It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods. In this paper, a new class of low-discrepancy sequences $N_\beta$ is constructed by using the ergodic theoretical transformation which is called β-adic transformation. Here, β is a real number greater than 1. When β is an integer greater than 2, $N_\beta$ becomes the classical van der Corput sequence in base β. Therefore, the class $N_\beta$ can be regarded as a generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the fastest order $O(N^{-1}\log N)$. We give the numerical results of discrepancy of Nβ for some βs.
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