  We report on the latest results of a Parkes multibeam survey for pulsars and
dispersed radio bursts in the Large Magellanic Cloud (LMC). We conducted both
periodicity and single-pulse searches at a much larger range of trial
dispersion measures (DMs) than previously searched. We detected 229 single
pulses with signal-to-noise ratio ($\rm{S/N}) > 7$ that were classified by the
deep learning network FETCH as being real (with $> 90$% likelihood), of which 9
were from the known giant-pulse-emitting pulsar PSR B0540$-$69. Two possibly
repeating sources were detected with DMs suggesting that they lie within the
LMC, but these require confirmation. Only 3 of the 220 unknown pulses had S/N
greater than 8, and the DM distribution for these detected pulses follows an
exponential falloff with increasing DM and does not show any excess of signals
at DM values expected for the LMC. These features suggest that the detected
pulses are not likely to be real, although they are visually compelling. We
also report the discovery of a new pulsar (PSR J0556$-$67) in our periodicity
search. This pulsar has a spin period of 791 ms, a DM of 71 cm$^{-3}$ pc, an
estimated 1400 MHz flux density of $\sim 0.12$ mJy, and shows no evidence of
binary motion. Future observations may be able to confirm whether any of the
weak but promising candidates in our single pulse and periodicity searches,
including our two possible repeaters, are real or not.
