  The quantum Hall plateau transition was studied at temperatures down to 1 mK
in a random alloy disordered high mobility two-dimensional electron gas. A
perfect power-law scaling with \kappa=0.42 was observed from 1.2K down to 12mK.
This perfect scaling terminates sharply at a saturation temperature of
T_s~10mK. The saturation is identified as a finite-size effect when the quantum
phase coherence length (L_{\phi} ~ T^{-p/2}) reaches the sample size (W) of
millimeter scale. From a size dependent study, T_s \propto W^{-1} was observed
and p=2 was obtained. The exponent of the localization length, determined
directly from the measured \kappa and p, is \nu=2.38, and the dynamic critical
exponent z = 1.
