A Finite-Row Scrambling of Niederreiter Sequences

Abstract

This paper introduces a scrambling matrix that modifies the generating matrices of the classical Niederreiter sequences to so-called finite-row generating matrices. The method used for determining this scrambling matrix also allows us to construct the inverse matrices of these generating matrices of Niederreiter. The question for finite-row digital (t, s)-sequences is motivated in the context of Niederreiter-Halton sequences, where—inspired by the Halton sequences—Niederreiter sequences in different bases are combined to a higher dimensional sequence. The investigation of the discrepancy of the Niederreiter-Halton sequences is a difficult task and still in its infancy. Results achieved for special examples raised the idea that the combination of finite-row generating matrices in different bases may be interesting. This paper also contains experiments that compare the performance of some Niederreiter-Halton sequences to the performance of Faure and Halton sequences and corroborate this idea.