Abstract
It is shown that among all tight designs in \({\mathbb {FP}^n \neq \mathbb {RP}^1}\) , where \({\mathbb {F}}\) is \({\mathbb {R}}\) or \({\mathbb {C}}\) , or \({\mathbb {H}}\) (quaternions), only 5-designs in \({\mathbb {CP}^1}\) (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) 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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Lyubich, Y.I. On tight projective designs. Des. Codes Cryptogr. 51, 21–31 (2009). https://doi.org/10.1007/s10623-008-9240-4
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DOI: https://doi.org/10.1007/s10623-008-9240-4