Kang–Kelly–Kühn–Methuku–Osthus random design existence conjecture

Let $\mathcal{G}^{(q)}(n,p)$ be the random $q$-uniform hypergraph on $n$ vertices, and let an $(n,q,r)$-Steiner system be a collection of $q$-sets containing every $r$-set exactly once. Kang–Kelly–Kühn–Methuku–Osthus conjecture. For every $q>r$, if

$$\binom{q-i}{r-i}\mid\binom{n-i}{r-i}$$

for all $i\in\{0,\dots,r-1\}$ and $p=\omega(n^{-q+r}\log n)$, then asymptotically almost surely $\mathcal{G}^{(q)}(n,p)$ contains an $(n,q,r)$-Steiner system. This is the upper-bound formulation of the conjectured random threshold, and the source gives no resolution status.