Zauner's conjecture for complex equiangular lines

Let $d\geq 2$. An equiangular line system in $\mathbb{C}^d$ is a set of lines through the origin whose unit-norm representatives have constant squared pairwise inner-product magnitude. Zauner's conjecture. For every $d\geq 2$, there exist $d^2$ equiangular lines in $\mathbb{C}^d$. This is the complex analogue of saturation of Gerzon's bound and remains open in general, although many dimensions are known.