Traditionally, optimality and uniqueness of an (n,N,t) spherical code is proved using linear programming bounds. However, this approach does not apply to the parameter (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code (which are the vertices of the 4-dimensional second hypersimplex or 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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Cornell University Library e-Print archive
Semidefinite programming and combinatorial optimization , Spinoza prijs Lex Schrijver
Networks and Optimization

Bachoc, C, & Vallentin, F. (2007). Optimality and uniqueness of the (4,10,1/6) spherical code. e-Print archive. Cornell University Library .