### Constraints on $\alpha$

We now use Equation \[eqn:eventrate\] along with the survey parameters mentioned in Table 2 to constrain $\alpha$. While doing so, we are invariably extrapolating the source counts computed from one fluence regime to another since different telescopes have different detection thresholds. We must thus carefully consider possible turn-overs or cut-offs in the source population towards large fluences.\
As will be shown in Section \[subsec:optimum\_dish\], for $\alpha<1$, a survey with a smaller dish (larger FOV) will detect more events as compared to one with a larger dish. Since the Parkes multiple-beam detection rates imply $\alpha\lesssim 1$, it is important to consider the (non-)detections from the ASSERT survey [@saint2014], which among published rate-limits at L-band has both the largest exposure time and the smallest dish. Since ASSERT found no FRBs, we make the reasonable assumption that there is a maximum FRB fluence cut-off at about $50$kJyms— consistent with the sensitivity of the ASSERT program. In addition, the inferred fluence of the brightest event observed thus far sets a lower limit on the maximum cut-off fluence. Based on modeling of the ‘Lorimer burst’ event at Parkes [@lorimer2007], the intrinsic fluence of the brightest Parkes burst is expected to be, 