A tight lower bound on the minimal dispersion

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00374661" target="_blank" >RIV/68407700:21340/24:00374661 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/10467/114258" target="_blank" >http://hdl.handle.net/10467/114258</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2024.103945" target="_blank" >10.1016/j.ejc.2024.103945</a>

Result language
angličtina
Original language name
A tight lower bound on the minimal dispersion
Original language description
We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very small class of test boxes, which allows us to reduce bounding the dispersion to a problem in extremal set theory. Specifically, we translate a lower bound on the size of r-cover-free families to a lower bound on the inverse of the minimal dispersion of a point set. The lower bound we obtain matches the recently obtained upper bound on the minimal dispersion up to logarithmic terms.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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