Optimality and uniqueness of the (4,10,1/6) spherical code
arXiv:0708.3947 · doi:10.1016/j.jcta.2008.05.001
Abstract
Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code, which consists of the midpoints of the edges of the regular simplex in dimension 4, is the unique (4,10,1/6) spherical code.
12 pages, (v2) several small changes and corrections suggested by referees, accepted in Journal of Combinatorial Theory, Series A
References in corpus (5)
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- Experimental study of energy-minimizing point configurations on spheres
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- Three-point bounds for energy minimization
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- Apollonian Ball Packings and Stacked Polytopes
- Linear programming bounds for regular graphs
- Finding and investigating exact spherical codes
- An extension the semidefinite programming bound for spherical codes
- Nonexistence of tight spherical design of harmonic index 4