Abstract
Given a sphere of any radius r in an n-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average number of solid spheres covering a point in a bigger sphere. For growing dimension n, we design a covering that gives the covering density of order (nln n)/2 for a sphere of any radius r>1 and a complete Euclidean space. This new upper bound reduces two times the order nln n established in the classic Rogers bound.
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Dumer, I. Covering Spheres with Spheres. Discrete Comput Geom 38, 665–679 (2007). https://doi.org/10.1007/s00454-007-9000-7
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DOI: https://doi.org/10.1007/s00454-007-9000-7