Duality for digital sequences

Authors:
Josef Dick;Harald Niederreiter
Affiliations:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia;RICAM University of Linz, Altenbergerstr. 69 A-4040, Linz, Austria and Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34 A-5020, Salzburg, Austria
Venue:
Journal of Complexity
Year:
2009

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Abstract

A duality theory for digital nets, i.e., for finite point sets with strong uniformity properties, was introduced by Niederreiter and Pirsic. This duality theory is based on the concept of the dual space M of a digital net. In this paper we extend the duality theory from (finite) digital nets to (infinite) digital sequences. The analogue of the dual space is now a chain of dual spaces (M"m)"m"="1 for which a certain projection of M"m"+"1 is a subspace of M"m. As an example of the use of dual space chains, we show how a well-known construction of digital sequences by Niederreiter and Xing can be achieved in a simpler manner by using our duality theory for digital sequences.