Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].
On tight projective designs
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abstract
It is shown that among all tight designs in FP^n, where F is R, C, or H (quaternions), other than RP^1, only 5-designs in CP^1 have irrational angle set. This is the only case of equal ranks of the first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
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Optimal measures for p-frame energies on spheres
Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].