Increasing stencils: the geometric escape

The additive rounding error is independent of $k$. The anisotropy term grows as $k{\epsilon }_n$; the whole error is not independent of $k$.

One tick reaches $h_n(S_n\cup \{0\})$, not every lattice point in ${\epsilon }_n{P}_n$. For example, with $S=\{\pm 1,\pm 3\}$, the point $2$ lies in $\mathrm{conv}(S)$ but is not reachable in one word step.