  We calculate numerically the localization length critical index within the
Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum
Hall effect. Lyapunov exponents have been calculated with relative errors on
the order $10^{-3}$. Such high precision was obtained by considering the
distribution of Lyapunov exponents for large ensembles of relatively short
chains and calculating the ensemble average values. We analyze thoroughly
finite size effects and find the localization length critical index $\nu=
2.517\pm 0.018$.
