A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 44

We give a new upper bound for the cardinality of a set of equiangular lines in RnRn with a fixed common angle θθ for each (n,θ)(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 44 on a sphere in RnRn with n≥3n≥3.