  The Milky Way's (MW) satellite population is a powerful probe of warm dark
matter (WDM) models as the abundance of small substructures is very sensitive
to the properties of the WDM particle. However, only a partial census of the
MW's complement of satellite galaxies exists because surveys of the MW's close
environs are incomplete both in depth and in sky coverage. We present a new
Bayesian analysis that combines the sample of satellites recently discovered by
the Dark Energy Survey (DES) with those found in the Sloan Digital Sky Survey
(SDSS) to estimate the total satellite galaxy luminosity function down to
$M_{\rm V}=0$. We find that there should be at least $124^{+40}_{-27}$ ($68\%$
CL, statistical error) satellites as bright or brighter than $M_{\rm V}=0$
within 300 kpc of the Sun, with only a weak dependence on MW halo mass. When it
comes online the Large Synoptic Survey Telescope should detect approximately
half of this population. We also show that WDM models infer the same number of
satellites as in $\Lambda$CDM, which will allow us to rule out those models
that produce insufficient substructure to be viable.
