  We consider periodic single-photon sources with combined multiplexing in
which the outputs of several time-multiplexed sources are spatially
multiplexed. We give a full statistical description of such systems in order to
optimize them with respect to maximal single-photon probability. We carry out
the optimization for a particular scenario which can be realized in bulk optics
and its expected performance is potentially the best at the present state of
the art. We find that combined multiplexing outperforms purely spatially or
time multiplexed sources for certain parameters only, and we characterize these
cases. Combined multiplexing can have the advantages of possibly using less
nonlinear sources, achieving higher repetition rates, and the potential
applicability for continuous pumping. We estimate an achievable single-photon
probability between 85% and 89%.
