  In this document we describe a model of an array of water Cherenkov detectors
proposed to study ultra-high-energy gamma rays in the southern hemisphere, and
a continuous model of secondary particles produced on the ground from gamma and
proton showers. We use the model of the detector and the parametrization of
showers for the identification of the most promising configuration of detector
elements, using a likelihood ratio test statistic to classify showers and a
stochastic gradient descent technique to maximize a utility function describing
the measurement precision on the gamma-ray flux.
