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We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, , is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show...
The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field with an s × m matrix C over . More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of . This paper introduces so-called Vandermonde nets, which correspond to Vandermonde-type matrices C, and discusses the quality parameter and the discrepancy of such nets. The methods that have been successfully used for the investigation...
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