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.KeywordsUnit SphereLinear CodeIntersection NumberMinimal NormDistance DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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