  We compute the perturbative expression of Wilson loops up to order $g^4$ for
SU($N$) lattice gauge theories with Wilson action on a finite box with twisted
boundary conditions. Our formulas are valid for any dimension and any
irreducible twist. They contain as a special case that of the 4-dimensional
Twisted Eguchi-Kawai model for a symmetric twist with flux $k$. Our results
allow us to analyze the finite volume corrections as a function of the flux. In
particular, one can quantify the approach to volume independence at large $N$
as a function of flux $k$. The contribution of fermion fields in the adjoint
representation is also analyzed.
