Existence conjecture for Steiner systems

Let $n>q>r\geq 1$ be integers. An $(n,q,r)$-Steiner system is a collection of $q$-subsets of an $n$-element set such that every $r$-subset is contained in exactly one member. Equivalently, it is a decomposition of the complete $r$-uniform hypergraph $K_n^r$ into copies of $K_q^r$. Existence conjecture for Steiner systems. For all integers $q>r\geq 1$, if $n$ is sufficiently large and

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

for each $0\leq i\leq r-1$, then an $(n,q,r)$-Steiner system exists. Keevash proved this conjecture for all sufficiently large $n$ satisfying the necessary divisibility conditions, so the conjecture is solved.