incompleteness at low fluence levels.\
A flatter log$N$-log$F$ distribution that yields many bright events also makes telescope sensitivity less important than the field of view, i.e., a smaller dish may discover more FRBs than a larger one! Many authors have reported (non-)detections from telescopes with varying dish sizes [@siemion2012; @spitler2014; @saint2014; @law2015] at L-band (around 1.4 GHz). The common frequency band used by these surveys allows us to compute their respective detection rates in a way that is largely independent of the inherent spectral or scattering properties of FRBs. We refine our Parkes multi-beam constraints with independent bounds on the value of $\alpha$ from such (non-)detections (Section \[sec:alpha\_mt\]).\
Finally, we discuss the implications of our bounds on $\alpha$ (Section \[sec:disc\]). The inconsistency we find of the FRB log$N$-log$F$ distribution with a non-evolving source population in Euclidean space has some important implications. To explore these implications, we consider a simple scenario where the FRB population cuts-off at some minimum and/or maximum distance. We find that FRB detection rates are either unbiased with or weighted towards larger distances to the progenitors. This bodes well for the use of FRBs as cosmological probes, even with telescopes with modest collecting areas.

Multiple-beam detection statistics 