  $ \newcommand{\R}{\ensuremath{\mathbb{R}}} \newcommand{\lat}{\mathcal{L}}
\newcommand{\ensuremath}[1]{#1} $We show that \[ \mu(\lat) \lambda_1(\lat^*) <
\big( 0.1275 + o(1) \big) \cdot n \; , \] where $\mu(\lat)$ is the covering
radius of an $n$-dimensional lattice $\lat \subset \R^n$ and
$\lambda_1(\lat^*)$ is the length of the shortest non-zero vector in the dual
lattice $\lat^*$. This improves on Banaszczyk's celebrated transference theorem
(Math. Annal., 1993) by about 20%.
  Our proof follows Banaszczyk exactly, except in one step, where we replace a
Fourier-analytic bound on the discrete Gaussian mass with a slightly stronger
bound based on packing. The packing-based bound that we use was already proven
by Aggarwal, Dadush, Regev, and Stephens-Davidowitz (STOC, 2015) in a very
different context. Our contribution is therefore simply the observation that
this implies a better transference theorem.
