On the intriguing search for good permutations

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Abstract

The intriguing search for permutations that generate generalised
van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s
80th birthday we aim to survey (some of) his contributions over the last four
decades which considerably improved our understanding of one-dimensional van
der Corput sequences and inspired a lot of related work. We recall and compare
the different approaches in the search for generalised van der Corput sequences
with low discrepancy, i.e., using a single generating permutation versus using
a sequence of permutations. Throughout, we collect, sharpen and extend open
questions which all stem from the extensive work of Henri and his coworkers and
which will hopefully inspire more work in the future.
Original languageEnglish
Pages (from-to)53-86
JournalUniform Distribution Theory
Volume14
Issue number1
DOIs
Publication statusPublished - Jan 2019

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