  For N>4 there is a first order bulk transition that cleanly separates the
strong and weak coupling regimes of SU(N) lattice gauge theories with the
plaquette action. We find that in this case the calculated string tension can
be readily fitted throughout the weak coupling region by a standard 3-loop
perturbative expression modified by lattice spacing corrections of the expected
form. While our fits demand the presence of the latter, they are not
constraining enough to tell us which of the various bare coupling schemes is a
`good' one, in the sense that terms in the beta-function beyond 3-loops are
indeed negligible (in the relevant range of scales). To resolve this ambiguity
we work in SU(3), using the Schrodinger Functional coupling scheme as a
benchmark, and find that the Parisi mean-field improved coupling scheme matches
it very well. Using the latter scheme, we have fitted the values of the string
tension that have been calculated for SU(3) to SU(8), to obtain
Lambda_MSbar/sqrt(sigma) = 0.503(2)(40) + 0.33(3)(3)/N**2, where the first
error is statistical and the second is our estimate of the systematic error
from all sources.
