The minimum codegree threshold for resolvable Steiner triple systems

Let $n$ be sufficiently large with $n\equiv 3\pmod{6}$, and let $H$ be a hypergraph on $n$ vertices. A resolvable Steiner triple system is a Steiner triple system whose triples can be partitioned into perfect matchings. The resolvable Steiner triple system conjecture. There are constants $n_0$ and $C$ such that, whenever $n\ge n_0$ and $H$ has minimum codegree at least $(3/4)n+C$, the hypergraph $H$ contains a resolvable Steiner triple system. Resolvable Steiner triple systems exist on $n$ vertices exactly when $n\equiv3\pmod 6$, but the asserted minimum-codegree threshold remains open.