Abstract
We show that there is essentially only one way of arranging 240 (resp. 196560) nonoverlapping unit spheres in R 8 (resp. R 24) so that they all touch another unit sphere Ω n , and only one way of arranging 56 (resp. 4600) spheres in R 8 (resp. R 24) so that they all touch two further, touching spheres. The following tight spherical t-designs are also unique: the 5-design in Ω7, the 7-designs in Ω8 and Ω23 and the 11-design in Ω24.
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© 1993 Springer Science+Business Media New York
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Bannai, E., Sloane, N.J.A. (1993). Uniqueness of Certain Spherical Codes. In: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, vol 290. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2249-9_14
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DOI: https://doi.org/10.1007/978-1-4757-2249-9_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2251-2
Online ISBN: 978-1-4757-2249-9
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