  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 $eV\gg k_{B}T$), 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.
