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.
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Academic Press
Journal of Combinatorial Theory - Series A
Networks and Optimization

Bachoc, C, & Vallentin, F. (2009). Optimality and uniqueness of the (4,10,1/6) spherical code. Journal of Combinatorial Theory - Series A, 116(1), 195–204.