Recently, there have been reports of six bright, dispersed bursts of coherent radio emission found in pulsar surveys with the Parkes Multi-beam Receiver. Not much is known about the progenitors of these bursts, but they are highly-energetic, and probably of extragalactic origin. Their properties suggest extreme environments and interesting physics, but in order to understand and study these events, more examples need to be found. Fortunately, the recent boom in radio astronomy means many next-generation radio telescopes are set to begin observing in the near future. In this paper we discuss the prospects of detecting short extragalactic bursts, in both beamformed and imaging data, using these instruments. We find that often the volume of space probed by radio surveys of fast transients is limited by the dispersion measure (DM) of the source, rather than its physical distance (although the two quantities are related). This effect is larger for low-frequency telescopes, where propagation effects are more prominent, but, their larger fields-of-view are often enough to compensate for this. Our simulations suggest that the low-frequency component of SKA1 could find an extragalactic burst every hour. We also show that if the sensitivity of the telescope is above a certain threshold, imaging surveys may prove more fruitful than beamformed surveys in finding these sorts of transients.
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