Using a three-level algorithm we perform a high-precision lattice computation
of the static force up to 1fm in the 2+1 dimensional SU(5) gauge theory.
Discretization errors and the continuum limit are discussed in detail. By
comparison with existing SU(2) and SU(3) data it is found that \sigma
r_0^2=1.65-\pi/24 holds at an accuracy of 1% for all N>=2, where r_0 is the
Sommer reference scale. The effective central charge c_{eff}(r) is obtained and
an intermediate distance r_s is defined via the property c_{eff}(r_s)=\pi/24.
It separates in a natural way the short-distance regime governed by
perturbation theory from the long-distance regime described by an effective
string theory. The ratio r_s/r_0 decreases significantly from SU(2) to SU(3) to
SU(5), where r_s < r_0. We give a preliminary estimate of its value in the
large-N limit. The static force in the smallest representation of N-ality 2,
which tends to the k=2 string tension as r->oo, is also computed up to 0.7fm.
The deviation from Casimir scaling is positive and grows from 0.1% to 1% in
that range.Comment: 25 pages, 8 figures, 11 table