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The Three-Dimensional Erdős Box Problem Has Exponent $11/4$
The Zarankiewicz problem for $3$-uniform hypergraphs asks for the maximum number $z(n)$ of edges in a tripartite hypergraph with $n$ vertices in each part containing no copy of $K_{2,2,2}^{(3)}$ (a ``box''). Erdős (1964) proved $z(n) = O(n^{11/4})$. The best previously known lower bound was $Ω(n^{8/
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