Remark: Notation and normalization

The physical word ball is

It is not $h_n{B}_{d_n}(0,k)$; the latter would rescale twice.

The one-tick reach is at most ${\epsilon }_n$, not necessarily exactly ${\epsilon }_n$, since the stencil need not contain a vector of length exactly $L_n$. Accordingly, $c$ is an exact upper normalization and an asymptotically attained speed.