The stabilization problem of a networked control system under data rate constraints and random packet losses is investigated. In addition to the communication constraints, plant uncertainty is explicitly considered. For a linear parametrically uncertain plat, we show a necessary condition to make the plant output mean square stable, which gives fundamental limitations on data rate, packet loss probabilities, and magnitudes of uncertainty. It is shown that the quantizer which has specific nonuniform cells can achieve stability with a lower data rate compared with the well-known uniform one. A sufficient condition is also given, which is equivalent to the necessary one when the plant is a scalar (one dimensional) system.