  We have used modern supercomputer facilities to carry out extensive Monte
Carlo simulations of 2D hopping (at negligible Coulomb interaction) in
conductors with the completely random distribution of localized sites in both
space and energy, within a broad range of the applied electric field $E$ and
temperature $T$, both within and beyond the variable-range hopping region. The
calculated properties include not only dc current and statistics of localized
site occupation and hop lengths, but also the current fluctuation spectrum.
Within the calculation accuracy, the model does not exhibit $1/f$ noise, so
that the low-frequency noise at low temperatures may be characterized by the
Fano factor $F$. For sufficiently large samples, $F$ scales with conductor
length $L$ as $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, and
parameter $L_c$ is interpreted as the average percolation cluster length. At
relatively low $E$, the electric field dependence of parameter $L_c$ is
compatible with the law $L_c\propto E^{-0.911}$ which follows from directed
percolation theory arguments.
