  We analyze the exact formulae for the resistance between two arbitrary notes
in a rectangular network of resistors under free, periodic and cylindrical
boundary conditions obtained by Wu [J. Phys. A 37, 6653 (2004)]. Based on such
expression, we then apply the algorithm of Ivashkevich, Izmailian and Hu [J.
Phys. A 35, 5543 (2002)] to derive the exact asymptotic expansions of the
resistance between two maximum separated nodes on an $M \times N$ rectangular
network of resistors with resistors $r$ and $s$ in the two spatial directions.
Our results is $ \frac{1}{s}R_{M\times N}(r,s)= c(\rho)\,
\ln{S}+c_0(\rho,\xi)+\sum_{p=1}^{\infty} \frac{c_{2p}(\rho,\xi)}{S^{p}} $ with
$S=M N$, $\rho=r/s$ and $\xi=M/N$. The all coefficients in this expansion are
expressed through analytical functions. We have introduced the effective aspect
ratio $\xi_{eff} = \sqrt{\rho}\;\xi$ for free and periodic boundary conditions
and $\xi_{eff} = \sqrt{\rho}\;\xi/2$ for cylindrical boundary condition and
show that all finite size correction terms are invariant under transformation
$\xi_{eff} \to {1}/\xi_{eff}$.
