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.
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