  PSR J0537-6910 is a young, energetic, rotation-powered X-ray pulsar with a
spin period of 16 ms located in the Large Magellanic Cloud. We have searched
for previously undetected radio pulsations (both giant and standard) from this
pulsar in a 12-hour observation taken at 1400 MHz with the Parkes 64-m radio
telescope. The very large value of the magnetic field at the light cylinder
radius suggests that this pulsar might be emitting giant radio pulses like
those seen in other pulsars with similar field strengths. No radio emission of
either kind was detected from the pulsar, and we have established an upper
limit of ~ 25 mJy kpc^2 for the average 1400-MHz radio luminosity of PSR
J0537-6910. The 5-sigma single-pulse detection threshold was ~ 750 mJy for a
single 80-us sample. These limits are likely to be the best obtainable until
searches with greatly improved sensitivity can be made with next-generation
radio instruments.
