منابع مشابه
Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy
We introduce a new construction method for digital nets which yield point sets in the s-dimensional unit cube with small star discrepancy. The digital nets are constructed using polynomials over finite fields. It has long been known that there exist polynomials which yield point sets with small (unweighted) star discrepancy. This result was obtained by Niederreiter by the means of averaging ove...
متن کاملDiscrepancy of hyperplane nets and cyclic nets
Digital nets are very important representatives in the family of lowdiscrepancy 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 we...
متن کاملThe Discrepancy of Digital Nets
Digital sequences and nets are among the most popular kinds of low discrepancy sequences and are often used for quasi-Monte Carlo quadrature rules. Several years ago Owen proposed a method of scrambling digital sequences and recently Faure and Tezuka have proposed another method. This article considers the discrepancy of digital nets under these scramblings. The first main result of this articl...
متن کاملOn the mean square weighted L2 discrepancy of randomized digital nets in prime base
We study the mean square weighted L2 discrepancy of randomized digital (t,m, s)nets over Zp. The randomization method considered here is a digital shift of depth m, i.e., for each coordinate the first m digits of each point are shifted by the same shift whereas the remaining digits in each coordinate are shifted independently for each point. We also consider a simplified version of this shift. ...
متن کاملTractability properties of the weighted star discrepancy
Tractability properties of various notions of discrepancy have been intensively studied in the last decade. In this paper we consider the so-called weighted star discrepancy which was introduced by Sloan and Woźniakowski. We show that under a very mild condition on the weights one can obtain tractability with s-exponent zero (s is the dimension of the point set). In the case of product weights ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-85-2-141-156