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We give an exact formula for the L2 discrepancy of two-dimensional digitally shifted Hammersley point sets in base b. This formula shows that for certain bases b and certain shifts the L2 discrepancy is of best possible order with respect to the general lower bound due to Roth. Hence, for the first time, it is proved that, for a thin, but infinite subsequence of bases b starting...
Digital nets are very important representatives in the family of low-discrepancy point sets which are often used as underlying nodes for quasi-Monte Carlo integration rules. Here we consider a special sub-class of digital nets known as cyclic nets and, more general, hyperplane nets. We show the existence of such digital nets of good quality with respect to star discrepancy in the classical as well...
Summary We present a new technique to estimate the star discrepancy of digital nets and sequences which is based on an analysis of the Walsh series of the discrepancy function.
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