Discrete & Computational Geometry

, Volume 33, Issue 1, pp 143-155

First online:

Covering a Ball with Smaller Equal Balls in ℝn

  • Jean-Louis Verger-GaugryAffiliated withInstitut Fourier, University of Grenoble I, UMR5582 (UJF-CNRS), BP 74, 38402 St. Martin d’Hères Cedex Email author 

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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.