Conjecture on the merit factor of Sidelnikov sequences

Let $q$ be an odd prime power, let $\theta$ be primitive in $\mathbb{F}_q$, and let $Z_{n,\theta}$ be the Sidelnikov sequence of length $n=q-1$ with respect to $\theta$. Let $F$ denote merit factor, and let $h(T)$ be the asymptotic function for Galois sequences specified in the source's Theorem 2.2(i). Sidelnikov merit factor conjecture. For each odd prime power $q$, choose an integer $r$ and a primitive $\theta\in\mathbb{F}_q$. If $T>0$ and $t/n\to T$ as $n\to\infty$, then

$$F\bigl(Z_{n,\theta}^{r,t}\bigr)\to h(T)$$

as $n\to\infty$. Numerical evidence motivates the conjecture, and the source does not provide a proof or resolution.