Mixon's divisibility conjecture for complex equiangular tight frames

Let $d$ and $n$ be positive integers. An $n$-vector equiangular tight frame in $\mathbb{C}^d$ is a set of $n$ equiangular unit vectors spanning $\mathbb{C}^d$ and satisfying the tight-frame condition. Consider the quantities

$$d, \qquad n-d, \qquad n-1.$$

Mixon's divisibility conjecture. There exists an $n$-vector equiangular tight frame in $\mathbb{C}^d$ only if one of these quantities divides the product of the other two.

This conjecture, posed by the first author at Sampling Theory and Applications 2015, seeks necessary conditions for the existence of complex equiangular tight frames, for which strong dimension restrictions were lacking compared with the real case. Its status is not resolved in the supplied source context.