FRB characteristics lends credibility to our results despite these misgivings.

Discussion {#sec:disc}
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The Parkes multiple-beam detection rates and the non-detections at other facilities strongly favor an FRB distribution that has a remarkably flat log$N$-log$F$ distribution: $0.66<\alpha<0.96$ (90% confidence) as compared to that expected in a Euclidean Universe $(\alpha=1.5$) with a non-evolving source population. This has implications both for design of future surveys and for theories regarding the progenitor population. We discuss these aspects below.

Implications for survey design {#subsec:optimum_dish}
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![image](alpha_COMB.pdf){width="\linewidth"}

We will now compute the observed number of FRB-like events for a hypothetical array as a function of dish size (single pixel receiver). Our aim is to determine the ‘optimum’ dish-diameter to maximize the number of detections. Fig. \[fig:eventrate\] shows the number of detections per month computed using Equations \[eqn:th\_noise\] to \[eqn:airy\] for a (hypothetical) array of $10$ dishes whose outputs are incoherently combined to detect FRBs. We assume the following parameters: $T_{\rm sys}=60$ K, $\eta=0.6$, $\nu=1.5$ GHz, $\Delta\nu=500$ MHz, $\tau_{\rm ds}=1$ ms, $\tau_{\rm FRB} = 3$ ms, $\zeta=8$. The different curves are for different values of the log$N$-log$F$ slope parameter $\alpha$. We assume that the source-counts cut-off at fluence $\mathcal{F}_{\rm max}$, and that the source-count normalization is 