Complex ETF existence conjecture beyond twice the dimension

Let $D$ and $N$ be positive integers with $N>2D>2$, and let an $\operatorname{ETF}(D,N)$ denote a complex equiangular tight frame of $N$ vectors in dimension $D$. Call $(D,N)$ positive or negative when it satisfies the positive or negative conditions defined in the source. Complex ETF existence conjecture. An $\operatorname{ETF}(D,N)$ exists if and only if

$$N=D^2\quad\text{or}\quad \frac{D(D-1)}{N-1}\in\mathbb{Z}\quad\text{or}\quad (D,N)\text{ is positive or negative}.$$

This conjecture proposes that, beyond the cases $N=2D$, all known construction families and the displayed arithmetic or type conditions account exactly for complex ETF existence. The conjecture remains open; the known nonexistence of an $\operatorname{ETF}(3,8)$ shows that existence questions are nontrivial.