95% confidence, the expected number of detections improves with increasing number of subarrays. In addition, since the data rate of an interferometer with $N$ elements, scales as $N^2$, the data rate for $N_{\rm sub}$ subarrays scales as $N^{-1}_{\rm sub}$. This reduction in data rate opens up the possibility to employ larger bandwidths and shorter correlator integration-times further improving the sensitivity to detection. In Fig. \[fig:vla\_subarrays\], we compute the improvement in detection rates that we expect by using subarrays at the VLA. We have assumed that the reduced number of baselines will allow for an increased bandwidth of $\Delta\nu=750$ MHz and a reduced integration time $\tau_{\rm int}=2.5$ ms, as compared to the values of $\Delta\nu=256$ MHz, and $\tau_{\rm int}=5$ ms used by @law2015 [(no sub-arraying)]. We find that given our constraints on $\alpha$, detection rates with the VLA can be increased three-fold by using 8 subarrays.

Implications for FRB distances
------------------------------

### Euclidian-space calculation

First, our bounds on $\alpha$ strongly disfavor models where FRBs are standard candles, since in that case, the log$N$-log$F$ function will have a slope of $\alpha=1.5$ barring carefully contrived source population evolution with distance (see Appendix A3). Next, we consider cases where FRBs have an intrinsic burst 