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arXiv · 1210.7721

Halton-type sequences from global function fields

Harald Niederreiter·Anderson Siang Jing Yeo
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Abstract

For any prime power $q$ and any dimension $s$, a new construction of $(t,s)$-sequences in base $q$ using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of $(t,s)$-sequences that is not based on the digital method. The construction can also be put into the framework of the theory of $(u,e,s)$-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.

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Harald Niederreiter, Anderson Siang Jing Yeo. 2012-10-29. Halton-type sequences from global function fields. https://doi.org/10.1007/s11425-013-4623-z

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