  We report a limit on the ultra-high-energy neutrino flux based on a
non-detection of radio pulses from neutrino-initiated particle cascades in the
Moon, in observations with the Parkes radio telescope undertaken as part of the
LUNASKA project. Due to the improved sensitivity of these observations, which
had an effective duration of 127 hours and a frequency range of 1.2-1.5 GHz,
this limit extends to lower neutrino energies than those from previous lunar
radio experiments, with a detection threshold below 10^20 eV. The calculation
of our limit allows for the possibility of lunar-origin pulses being
misidentified as local radio interference, and includes the effect of
small-scale lunar surface roughness. The targeting strategy of the observations
also allows us to place a directional limit on the neutrino flux from the
nearby radio galaxy Centaurus A.
