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Does anyone know, how many points does one need to have an $\varepsilon$-net on a unit sphere sitting in the three-dimensional Euclidean space? Thanks!

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Cute problem. You could form an over-estimate by taking a uniform grid on the surface of a cube of side $2$ centered at $0$ and 'projecting' radially onto the sphere. If I have counted correctly, $6 k^2$ points would give a (better than) $\frac{\sqrt{3}}{k}$-net. But I have no idea how to compute the minimum number. – copper.hat Nov 16 '12 at 5:55
Do you want the exact minimum (probably not feasible), or some kind of asymptotics? It is pretty clear that the number grows like $C\epsilon^{-2}$, are you interested in the optimal $C$? – Lukas Geyer Nov 16 '12 at 23:22

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