Extension of van der Corput algorithm to LS-sequences

Abstract

The LS-sequences of points recently introduced by the author are a generalization of van der Corput sequences. They are constructed by reordering the points of the corresponding LS-sequences of partitions. Here we present another algorithm which is simpler to compute than the original construction and coincides with the classical one for van der Corput sequences. This algorithm is based on the representation of natural numbers in base L+S. Moreover, when S⩽L these sequences have low discrepancy and can be useful in Quasi Monte-Carlo methods.