Zauner's maximal equiangular tight frame conjecture

For each dimension $m$, let $\rho_1,\rho_2,\rho_3$ denote the three quantities defined in the paper, and let $\rho(m)$ be the associated complex projection constant. Zauner's conjecture. For every $m\geq 1$,

$$\lambda_\mathbb{C}(m)=\frac{1}{m}\left(1+(m-1)\sqrt{m+1}\right).$$

This is equivalent in the paper's framework to the existence of a complex maximal equiangular tight frame in every dimension. The formula is known in the listed dimensions $m\in\{1,\ldots,17,19,24,28,35,48\}$, while the assertion for every dimension remains open.