  Using the most recent prototypes, design, and as-built system information, we
test and quantify the capability of the Large Synoptic Survey Telescope (LSST)
to discover Potentially Hazardous Asteroids (PHAs) and Near-Earth Objects
(NEOs). We empirically estimate an expected upper limit to the false detection
rate in LSST image differencing, using measurements on DECam data and prototype
LSST software and find it to be about $450$~deg$^{-2}$. We show that this rate
is already tractable with current prototype of the LSST Moving Object
Processing System (MOPS) by processing a 30-day simulation consistent with
measured false detection rates. We proceed to evaluate the performance of the
LSST baseline survey strategy for PHAs and NEOs using a high-fidelity simulated
survey pointing history. We find that LSST alone, using its baseline survey
strategy, will detect $66\%$ of the PHA and $61\%$ of the NEO population
objects brighter than $H=22$, with the uncertainty in the estimate of $\pm5$
percentage points. By generating and examining variations on the baseline
survey strategy, we show it is possible to further improve the discovery
yields. In particular, we find that extending the LSST survey by two additional
years and doubling the MOPS search window increases the completeness for PHAs
to $86\%$ (including those discovered by contemporaneous surveys) without
jeopardizing other LSST science goals ($77\%$ for NEOs). This equates to
reducing the undiscovered population of PHAs by additional $26\%$ ($15\%$ for
NEOs), relative to the baseline survey.
