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Our analysis shows that we can exclude the presence of astrophysical transients on timescales of 5 milliseconds and below. We measured data quality at regular intervals throughout the search and found that roughly 1\% of images had noise that was more than twice the median image noise. Our flux-calibrated observations have a median image noise of 12--14 mJy, as expected for 5-ms, L-band images made with data from 26 good antennas and 230 MHz of bandwidth. To include variance in the noise measurements, we define a 96\% completeness for a $1\sigma$ image sensitivity of 15 mJy or an $8\sigma$ flux limit of 120 mJy. Observations of pulsar B0355+54 at a range of offset positions shows that imaging sensitivity scales as expected for the VLA primary beam gain pattern. This end-to-end test also confirms that our transient search pipeline works as expeted.  Figure \ref{rate_pub} summarizes the published FRB event rates and the VLA rate limit to FRBs shorter than our integration time of 5 ms. In constructing this figure, we discovered that the sensitivity of published surveys are defined inconsistently. \citet{2014arXiv1404.2934S} calculate the mean beam gain within the FWHM. Burke-Spolaor \& Bannister (2014, submitted; hereafter "BSB14") use half the main beam gain. \citet{2007Sci...318..777L} use the measured fluence of their detection to define a fluence limit. Finally, \citet{2013Sci...341...53T} don't report a fluence limit at all, but instead measure the mean fluence of all detections. For this figure, we use the mean primary  beam gain, as in \citet{2014arXiv1404.2934S}, although this clearly overestimates the sensitivity at the half-power point of the primary beam, point,  as demonstrated in our pulsar tests.