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We have searched three Parkes multibeam 1.4 GHz surveys for the presence offast radio bursts (FRBs) out to a dispersion measure (DM) of 5000 pc cm$^{-3}$.These surveys originally targeted the Magellanic Clouds (in two cases) andunidentified gamma-ray sources at mid-Galactic latitudes (in the third case)for new radio pulsars. In previous processing, none of these surveys weresearched to such a high DM limit. The surveys had a combined total of 719 hr ofParkes multibeam on-sky time. One known FRB, 010724, was present in our dataand was detected in our analysis but no new FRBs were found. After adding inthe on-sky Parkes time from these three surveys to the on-sky time (7512 hr)from the five Parkes surveys analysed by Rane et al., all of which have nowbeen searched to high DM limits, we improve the constraint on the all-sky rateof FRBs above a fluence level of 3.8 Jy ms at 1.4 GHz to $R = 3.3^{+3.7}_{-2.2}\times 10^{3}$ events per day per sky (at the 99% confidence level). FutureParkes surveys that accumulate additional multibeam on-sky time (such as theongoing high-resolution Parkes survey of the LMC) can be combined with theseresults to further constrain the all-sky FRB rate.

A Search for Highly Dispersed Fast Radio Bursts in Three Parkes Multibeam Surveys