Asymptotic upper-bound conjecture for wide-sense 2-frameproof codes

Let $Q$ be an alphabet and let $\mathcal{C}\subseteq Q^n$ be a wide-sense $2$-frameproof code of size $m$.

Wide-sense 2-frameproof code conjecture. For large $n$,

$$m=o\left(\binom{n}{\left\lfloor\frac{n-1}{2}\right\rfloor}\right).$$

The paper proves an upper bound of order $\binom{n}{\lfloor (n-1)/2\rfloor}$ and conjectures an exponential improvement, namely that the ratio to this binomial bound tends to zero. The source does not indicate a resolution.