Asymptotic threshold conjecture for wide-sense frameproof codes

Let $Q$ be an alphabet, and let $N_q(t)$ be the minimum $n\geq 2$ such that there exists a wide-sense $t$-frameproof code $\mathcal{C}\subseteq Q^n$ with $|\mathcal{C}|>n$.

Wide-sense frameproof threshold conjecture.

$$\lim_{t\rightarrow\infty}\frac{N_q(t)}{t^2}=1.$$

The paper states that this conjecture is equivalent, via the displayed comparison between $N^*(t-2)$, $N_q(t)$, and $N_2(t)$, to the weaker asymptotic form of the Erdős–Frankl–Füredi conjecture. The source does not indicate a resolution.