A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids

We construct a 2-parameter family of complex Hadamard matrices of order 6 by a natural block construction. We combine this family with an earlier result of Zauner to derive a 2-parameter family of triplets of mutually unbiased bases (MUBs) in ℂ 6 . This invalidates some numerical evidence given by Brierley and Weigert and sheds new light on the problem of determining the maximal number of MUBs in ℂ 6 .

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