  We conducted a volume-limited survey at 4.9 GHz of 32 nearby ultracool dwarfs
with spectral types covering the range M7 -- T8. A statistical analysis was
performed on the combined data from the present survey and previous radio
observations of ultracool dwarfs. Whilst no radio emission was detected from
any of the targets, significant upper limits were placed on the radio
luminosities that are below the luminosities of previously detected ultracool
dwarfs. Combining our results with those from the literature gives a detection
rate for dwarfs in the spectral range M7 -- L3.5 of ~ 9%. In comparison, only
one dwarf later than L3.5 is detected in 53 observations. We report the
observed detection rate as a function of spectral type, and the number
distribution of the dwarfs as a function of spectral type and rotation
velocity. The radio observations to date point to a drop in the detection rate
toward the ultracool dwarfs. However, the emission levels of detected ultracool
dwarfs are comparable to those of earlier type active M dwarfs, which may imply
that a mildly relativistic electron beam or a strong magnetic field can exist
in ultracool dwarfs. Fast rotation may be a sufficient condition to produce
magnetic fields strengths of several hundreds Gauss to several kilo Gauss, as
suggested by the data for the active ultracool dwarfs with known rotation
rates. A possible reason for the non-detection of radio emission from some
dwarfs is that maybe the centrifugal acceleration mechanism in these dwarfs is
weak (due to a low rotation rate) and thus cannot provide the necessary density
and/or energy of accelerated electrons. An alternative explanation could be
long-term variability, as is the case for several ultracool dwarfs whose radio
emission varies considerably over long periods with emission levels dropping
below the detection limit in some instances.
