Continuous Zauner's conjecture for equiangular tight continuous frames

Let $(\Omega,\mu)$ be a measure space, let $d\in\mathbb{N}$, and let $\{\tau_\alpha\}_{\alpha\in\Omega}$ be a continuous frame for the Hilbert space $\mathbb{C}^d$. The frame is $\gamma$-equiangular if there exists $\gamma\geq 0$ such that

$$|\langle\tau_\alpha,\tau_\beta\rangle|=\gamma,\qquad \forall\alpha,\beta\in\Omega,\ \alpha\neq\beta.$$

It is tight if its frame operator is a scalar multiple of the identity. Continuous Zauner's conjecture. For a given measure space $(\Omega,\mu)$ and for every $d\in\mathbb{N}$, there exists a $\gamma$-equiangular tight continuous frame $\{\tau_\alpha\}_{\alpha\in\Omega}$ for $\mathbb{C}^d$ such that $\mu(\Omega)=d^2$. This is the continuous analogue of Zauner's conjecture for equiangular tight frames; the existence assertion is posed for every dimension and measure space, and its resolution is not supplied here.