Abstract
We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n,θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥3.
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