  The lunar Cherenkov technique, which aims to detect the coherent Cherenkov
radiation produced when UHE particles interact in the lunar regolith, was first
attempted with the Parkes radio-telescope in 1995, though the theory was not
sufficiently developed at this time to calculate a limit on the UHE neutrino
flux from the non-observation. Since then, the technique has evolved to include
experiments utilising lower frequencies, wider bandwidths, and entire arrays of
antenna. We develop a simulation to analyse the full range of experiments, and
calculate the UHE neutrino flux limit from the Parkes experiment, including the
directional dependence. Our results suggest a methodology for planning future
observations, and demonstrate how to utilise all available information on the
nature of radio pulses from the Moon for the detection of UHE particles.
