We have derived a general formula describing current noise in multimode ballistic channels connecting source and drain electrodes with Fermi electron gas. In particular (at $eVgg k_{B}T$), the expression describes the nonequilibrium shot noise, which may be suppressed by both Fermi correlations and space charge screening. The general formula has been applied to an approximate model of a 2D nanoscale, ballistic MOSFET. At large negative gate voltages, when the density of electrons in the channel is small, shot noise spectral density $S_{I}(0)$ approaches the Schottky value $2eI$, where $I$ is the average current. However, at positive gate voltages, when the maximum potential energy in the channel is below the Fermi level of the electron source, the noise can be at least an order of magnitude smaller than the Schottky value, mostly due to Fermi effects.
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