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.
Linear programming, Semidefinite programming, Spherical codes, Spherical designs, Petersen graph
dimensions (msc 52C17), Semidefinite programming (msc 90C22)
Logistics (theme 3)
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.