English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We improve the best known upper bound for the bracketing number of$d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, oflower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$).More precisely, we provide a better upper bound for the cardinality of analgorithmic bracketing cover construction due to Eric Thi\'emard, which formsthe core of his algorithm to approximate the star discrepancy of arbitrarypoint sets from [E. Thi\'emard, An algorithm to compute bounds for the stardiscrepancy, J.~Complexity 17 (2001), 850 -- 880].  Moreover, the new upper bound for the bracketing number of anchoredaxis-parallel boxes yields an improved upper bound for the bracketing number ofarbitrary axis-parallel boxes in $[0,1]^d$.  In our upper bounds all constants are fully explicit.

Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thi\'{e}mard to compute bounds for the star discrepancy