  We present the results from a search for the electromagnetic counterpart of
the LIGO/Virgo event S190510g using the Dark Energy Camera (DECam). S190510g is
a binary neutron star (BNS) merger candidate of moderate significance detected
at a distance of 227$\pm$92 Mpc and localized within an area of 31 (1166)
square degrees at 50\% (90\%) confidence. While this event was later classified
as likely non-astrophysical in nature within 30 hours of the event, our short
latency search and discovery pipeline identified 11 counterpart candidates, all
of which appear consistent with supernovae following offline analysis and
spectroscopy by other instruments. Later reprocessing of the images enabled the
recovery of 6 more candidates. Additionally, we implement our candidate
selection procedure on simulated kilonovae and supernovae under DECam observing
conditions (e.g., seeing, exposure time) with the intent of quantifying our
search efficiency and making informed decisions on observing strategy for
future similar events. This is the first BNS counterpart search to employ a
comprehensive simulation-based efficiency study. We find that using the current
follow-up strategy, there would need to be 19 events similar to S190510g for us
to have a 99\% chance of detecting an optical counterpart, assuming a
GW170817-like kilonova. We further conclude that optimization of observing
plans, which should include preference for deeper images over multiple color
information, could result in up to a factor of 1.5 reduction in the total
number of followups needed for discovery.
