  We have used the VLA to conduct a deep search for 3.6 cm radio emission from
nearby very low mass stars and brown dwarfs. The Gudel-Benz relation is used to
predict radio luminosities for some very low mass stars and candidate brown
dwarfs with measured X-ray fluxes. The predicted radio fluxes are quite small,
whereas the measured radio flux from the brown dwarf candidate Rho Oph GY 31 is
relatively strong. In light of our new observations, this object remains an
anomaly. We present upper limits for our measured radio fluxes at 3.6 cm for
our targets.
