Abstract
In 1929 H.F. Blichfeldt discovered a remarkable method for determining an upper bound for δ(S n ). Roughly speaking, his idea runs as follows. Let S n + X be a packing and let r be a number such that r > 1. Then, replace the spheres S n + x, where x ∈ X, by rS n + x and fill each of these new spheres with a certain amount of mass, of variable density, such that the total mass at any point of En does not exceed 1. Hence, the total mass of the spheres rS n + x, where x ∈ X ∩ (l − r) I n , does not exceed the volume of the large cube lI n . In this way, Blichfeldt obtained the first significant upper bound for δ(S n ).
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© 1999 Springer-Verlag New York, Inc.
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(1999). Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres I. In: Talbot, J. (eds) Sphere Packings. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22780-1_6
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DOI: https://doi.org/10.1007/978-0-387-22780-1_6
Publisher Name: Springer, New York, NY
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