A new class of $s$-dimensional uniformly distributed sequences called the generalized van der Corput sequence is defined. The sequence is constructed by using the generalized number system based on an integer matrix whose all eigen values reside out of the unit circle. In this talk , we show that by using the generalized van der Corput sequence we can calculate numerical integrations with the convergence speed $O(1/N)$ when integrands stisfy some regularity conditions. We also apply the seqence to a numerical integration problem and test effectiveness of the sequence.
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