Abstract
We give an explicit upper bound of the minimal number νT,n of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in ℝn, n \geq 2. The asymptotic estimates of νT,n we deduce when n is large are improved further by recent results of Böröczky, Jr. and Wintsche on the asymptotic estimates of the minimal numberof equal balls of ℝn covering the sphere Sn-1. The optimality of the asymptotic estimates is discussed.
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Verger-Gaugry, JL. Covering a Ball with Smaller Equal Balls in ℝn. Discrete Comput Geom 33, 143–155 (2005). https://doi.org/10.1007/s00454-004-2916-2
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DOI: https://doi.org/10.1007/s00454-004-2916-2