  We conduct a search for radio stars by combining radio and optical data from
the Faint Images of the Radio Sky at Twenty cm survey (FIRST) and the Sloan
Digital Sky Survey (SDSS). The faint limit of SDSS makes possible a homogeneous
search for radio emission from stars of low optical luminosity. We select a
sample of 112 candidate radio stars in the magnitude range $15<i\lesssim19.1$
and with radio flux $S_{20}\geq1.25$mJy, from about 7000 deg$^2$ of sky. The
selection criteria are positional coincidence within $1\arcsec$, radio and
optical point source morphology, and an SDSS spectrum classified as stellar.
The sample contamination is estimated by random matching to be $108\pm13$,
suggesting that at most a small fraction of the selected candidates are genuine
radio stars. Therefore, we rule out a very rare population of extremely
radio-loud stars: no more than 1.2 of every million stars in the magnitude
range $15<i<19.1$ stars has radio flux $S_{20}\geq1.25$ mJy. We investigate the
optical and radio colors of the sample to find candidates that show the largest
likelihood of being real radio stars. The significant outliers from the stellar
locus, as well as the magnetically active stars, are the best candidates for
follow-up radio observations. We conclude that, while the present wide-area
radio surveys are not sensitive enough to provide homogeneous samples of the
extremely rare radio stars, upcoming surveys which exploit the great
sensitivity of current and planned telescopes do have sufficient sensitivity
and will allow the properties of this class of object to be investigated in
detail.
