Covering spheres with spheres

Details Covering spheres with spheres Covering spheres with spheres

2006-05-31

arxiv.org/abs/math/0606002v1

Mathematics

Metric Geometry

11 pages, 1 figure

Scientific paper

Given a sphere of radius $r>1$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing $n,$ we obtain the covering density of $(n\ln n)/2.$ This new upper bound is half the order $n\ln n$ established in the classic Rogers bound.

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