  We show nearly quadratic separations between two pairs of complexity
measures:
  1. We show that there is a Boolean function $f$ with
$D(f)=\Omega((D^{sc}(f))^{2-o(1)})$ where $D(f)$ is the deterministic query
complexity of $f$ and $D^{sc}$ is the subcube partition complexity of $f$;
  2. As a consequence, we obtain that there is a communication task $f(x, y)$
such that $D^{cc}(f)=\Omega(\log^{2-o(1)}\chi(f))$ where $D^{cc}(f)$ is the
deterministic 2-party communication complexity of $f$ (in the standard 2-party
model of communication) and $\chi(f)$ is the partition number of $f$.
  Both of those separations are nearly optimal: it is well known that
$D(f)=O((D^{sc}(f))^{2})$ and $D^{cc}(f)=O(\log^2\chi(f))$.
