We report the results of a volume-limited survey using the Australia Telescope Compact Array to search for transient and quiescent radio emission from 15 southern hemisphere ultracool dwarfs. We detect radio emission from 2MASSW J0004348-404405 increasing the number of radio loud ultracool dwarfs to 22. We also observe radio emission from 2MASS J10481463-3956062 and 2MASSI J0339352-352544, two sources with previous radio detections. The radio emission from the three detected sources shows no variability or flare emission. Modelling this quiescent emission we find that it is consistent with optically thin gyrosynchrotron emission from a magnetosphere with an emitting region radius of (1 - 2)$R_*$, magnetic field inclination 20$^{circ}$ - 80$^{circ}$, field strength $sim$10 - 200 G, and power-law electron density $sim$10$^4$ - 10$^8$ cm$^{-3}$. Additionally, we place upper limits on four ultracool dwarfs with no previous radio observations. This increases the number of ultracool dwarfs studied at radio frequencies to 222. Analysing general trends of the radio emission for this sample of 15 sources, we find that the radio activity increases for later spectral types and more rapidly rotating objects. Furthermore, comparing the ratio of the radio to X-ray luminosities for these sources, we find 2MASS J10481463-3956062 and 2MASSI J0339352-352544 violate the Guedel-Benz relation by more than two orders of magnitude.
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