We analyze a 19-night photometric search for transiting extrasolar planets in
the open cluster NGC 1245. An automated transit search algorithm with
quantitative selection criteria finds six transit candidates; none are bona
fide planetary transits. We characterize the survey detection probability via
Monte Carlo injection and recovery of realistic limb-darkened transits. We use
this to derive upper limits on the fraction of cluster members with close-in
Jupiter-radii, RJ, companions. We carefully analyze the random and systematic
errors of the calculation. For similar photometric noise and weather properties
as this survey, observing NGC 1245 twice as long results in a tighter
constraint on "Hot Jupiter", HJ, companions than observing an additional
cluster of similar richness as NGC 1245 for the same length of time as this
survey. This survey observed ~870 cluster members. If 1% of stars have 1.5 RJ
HJ companions, we expect to detect one planet for every 5000 dwarf stars
observed for a month. To reach a ~2% upper limit on the fraction of stars with
1.5 RJ HJ companions, we conclude a total sample size of ~7400 dwarf stars
observed for at least a month will be needed. Results for 1.0 RJ companions,
without substantial improvement in the photometric precision, will require a
small factor larger sample size.Comment: 24 pages, 15 figures, submitted A