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The set of points in a metric space is called an $s$-distance set if pairwise distances between these points admit only $s$ distinct values.
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Erdős-Ko-Rado theorem— 22 22 years later
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T. Okuda and W.-H. Yu, A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4 , European J. of Combin. Volume 53
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