$\newcommand{\popt}{\mathcal{p}} \newcommand{\Re}{\mathbb{R}}\newcommand{\N}{\mathcal{N}} \newcommand{\BX}{\mathcal{B}} \newcommand{\bb}{\mathsf{b}} \newcommand{\eps}{\varepsilon} \newcommand{\polylog}{\mathrm{polylog}} $ Let $\mathcal{B}=\{\mathsf{b}_1, \ldots ,\mathsf{b}_n\}$ be a set of $n$ axis-aligned boxes in $\Re^d$ where $d\geq2$ is a constant. The \emph{piercing problem} is to compute a smallest set of points $\N \subset \Re^d$ that hits every box in $\mathcal{B}$, i.e., $\N\cap \mathsf{b}_i\neq \emptyset…