Extremal hypergraphs without generalized 4-cycles

In 1977, Erdős posed the problem of determining the maximum number $f_r(n)$ of edges in an $n$-vertex $r$-uniform hypergraph in which all disjoint pairs of edges have distinct unions. Füredi later conjectured that, for every fixed $r\ge 4$ and all sufficiently large $n$, $f_r(n)=\binom{n-1}{r-1}+\lf