  We show that any bounded integral function $f : A \times B \mapsto \{0,1,
\dots, \Delta\}$ with rank $r$ has deterministic communication complexity
$\Delta^{O(\Delta)} \cdot \sqrt{r} \cdot \log r$, where the rank of $f$ is
defined to be the rank of the $A \times B$ matrix whose entries are the
function values. As a corollary, we show that any $n$-dimensional polytope that
admits a slack matrix with entries from $\{0,1,\dots,\Delta\}$ has extension
complexity at most $\exp(\Delta^{O(\Delta)} \cdot \sqrt{n} \cdot \log n)$.
