  Observations of the redshifted 21-cm line of atomic hydrogen have resulted in
several upper limits on the 21-cm power spectrum and a tentative detection of
the sky-averaged signal at $z\sim17$. Made with the EDGES Low-Band antenna,
this claim was recently disputed by the SARAS3 experiment, which reported a
non-detection and is the only available upper limit strong enough to constrain
cosmic dawn astrophysics. We use these data to constrain a population of
radio-luminous galaxies $\sim 200$ million years after the Big Bang ($z\approx
20$). We find, using Bayesian data analysis, that the data disfavours (at 68%
confidence) radio-luminous galaxies in dark matter halos with masses of
$4.4\times10^{5}$ M$_\odot \lesssim M \lesssim 1.1\times10^{7}$M$_\odot$ (where
$M_\odot$ is the mass of the Sun) at $z = 20$ and galaxies in which $>5$% of
the gas is converted into stars. The data disfavour galaxies with radio
luminosity per star formation rate of $L_\mathrm{r}/\mathrm{SFR} \gtrsim 1.549
\times 10^{25}$ W Hz$^{-1}$M$_\odot^{-1}$ yr at 150 MHz, a thousand times
brighter than today, and, separately, a synchrotron radio background in excess
of the CMB by $\gtrsim 6%$ at 1.42 GHz.
