  We consider digital expansions in lattices with endomorphisms acting as base.
We focus on the $w$-non-adjacent form ($w$-NAF), where each block of $w$
consecutive digits contains at most one non-zero digit. We prove that for
sufficiently large $w$ and an expanding endomorphism, there is a suitable digit
set such that each lattice element has an expansion as a $w$-NAF.
  If the eigenvalues of the endomorphism are large enough and $w$ is
sufficiently large, then the $w$-NAF is shown to minimise the weight among all
possible expansions of the same lattice element using the same digit system.
