Covering a Ball with Smaller Equal Balls in ℝn
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- Verger-Gaugry, JL. Discrete Comput Geom (2005) 33: 143. doi:10.1007/s00454-004-2916-2
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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.