  We present a linear program for the one-way version of the partition bound
(denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizes
one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with
shared randomness of every partial function
$f:\mathcal{X}\times\mathcal{Y}\to\mathcal{Z}$, i.e., for
$\delta,\varepsilon\in(0,1/2)$, $\mathsf{R}_\varepsilon^1(f) \geq
\log\mathsf{prt}_\varepsilon^1(f)$ and $\mathsf{R}_{\varepsilon+\delta}^1(f)
\leq \log\mathsf{prt}_\varepsilon^1(f) + \log\log(1/\delta)$. This improves
upon the characterization of $\mathsf{R}_\varepsilon^1(f)$ in terms of the
rectangle bound (due to Jain and Klauck, 2010) by reducing the additive
$O(\log(1/\delta))$-term to $\log\log(1/\delta)$.
