Erdős–Frankl–Füredi conjecture on the threshold for nontrivial cover-free families

Let $T(n,t)$ be the maximum cardinality of a $t$-cover-free family over an $n$-element underlying set. Let $N^*(t)$ be the minimum $n$ such that there exists a $t$-cover-free family $\mathcal{F}\subseteq 2^{[n]}$ with $|\mathcal{F}|>n$.

Erdős–Frankl–Füredi conjecture.

$$\lim_{t\rightarrow\infty}\frac{N^*(t)}{t^2}=1,$$

or, in the stronger form,

$$N^*(t)\geq (t+1)^2.$$

This conjecture concerns the smallest ground-set size at which a $t$-cover-free family can have more members than the size of its ground set. Its asymptotic form is closely related to determining the transition in the extremal function $T(n,t)$ and to group testing; the source does not indicate a resolution.