On an explicit lower bound for the star discrepancy in three dimensions

Florian Puchhammer

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 143, issue C, 158-168

Abstract: Following a result of D. Bylik and M.T. Lacey from 2008 it is known that there exists an absolute constant η>0 such that the (unnormalized) L∞-norm of the three-dimensional discrepancy function, i.e. the (unnormalized) star discrepancy DN∗, is bounded from below by DN∗≥c(logN)1+η, for all N∈N sufficiently large, where c>0 is some constant independent of N. This paper builds upon their methods to verify that the above result holds with η<1/(32+441)≈0.017357…

Keywords: Uniform distribution; Discrepancy; Number theory (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:143:y:2018:i:c:p:158-168

DOI: 10.1016/j.matcom.2016.08.006

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