On Proinov’s Lower Bound for the Diaphony

Nathan Kirk

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In 1986, Proinov published an explicit lower bound for the diaphony of both finite and infinite sequences of points in the d-dimensional unit cube. To the best of our knowledge, the proofs of these results were so far only available in a monograph of Proinov written in Bulgarian. The first contribution of our paper is to give a self contained version of Proinov's proof in English. Along the way, we improve the asymptotic constants using recent and corrected results of Hinrichs and Markhasin. Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.
Original languageEnglish
Article number4
Pages (from-to)39-72
Number of pages34
JournalUniform Distribution Theory
Issue number2
Publication statusPublished - 25 Dec 2020


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