  We are interested in numerical algorithms for computing the electrical field
generated by a charge distribution localized on scale $\ell$ in an infinite
heterogeneous medium, in a situation where the medium is only known in a box of
diameter $L\gg\ell$ around the support of the charge. We propose a boundary
condition that with overwhelming probability is (near) optimal with respect to
scaling in terms of $\ell$ and $L$, in the setting where the medium is a sample
from a stationary ensemble with a finite range of dependence (set to be unity
and with the assumption that $\ell \gg 1$). The boundary condition is motivated
by quantitative stochastic homogenization that allows for a multipole expansion
[BGO20].
  This work extends [LO21], the algorithm in which is optimal in two dimension,
and thus we need to take quadrupoles, next to dipoles, into account. This in
turn relies on stochastic estimates of second-order, next to first-order,
correctors. These estimates are provided for finite range ensembles under
consideration, based on an extension of the semi-group approach of [GO15].
