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 u=2.38, and the dynamic critical exponent z = 1.
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