  We present radio observations of a comprehensive sample of 90 dwarf stars and
brown dwarfs ranging from spectral type M5 to T8. We detect three radio active
sources in addition to the six objects previously detected in quiescence and
outburst, leading to an overall detection rate of about 10% for objects later
than M7. From the properties of the radio emission we infer magnetic field
strengths of ~100 G in quiescence and nearly 1 kG during flares, while the
majority of the non-detected objects have B<50 G. Depending on the
configuration and size of the magnetic loops, the surface magnetic fields may
approach 1 kG even in quiescence, at most a factor of few smaller than in
early-M dwarfs. With the larger sample of sources we find continued evidence
for (i) a sharp transition around spectral type M7 from a ratio of radio to
X-ray luminosity of log(L_R/L_X) ~ -15.5 to >-12, (ii) increased radio activity
with later spectral type, in contrast to H-alpha and X-ray observations, and
(iii) an overall drop in the fraction of active sources from about 30% for M
dwarfs to about 5% for L dwarfs, fully consistent with H-alpha and X-ray
observations. Taken together, these trends suggest that some late-M and L
dwarfs are capable of generating 0.1-1 kG magnetic fields, but the overall drop
in the fraction of such objects is likely accompanied by a change in the
structure of the chromospheres and coronae, possibly due to the increasingly
neutral atmospheres and/or a transition to a turbulent dynamo. A more extended
radio survey currently holds the best promise for measuring the magnetic field
properties of a large number of dwarf stars. [abridged]
