  We continue our study of heavy-light four-quark states and find evidence from
lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$
$ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below
$\bar{D}B^*$ threshold. Since this range includes the electromagnetic
$\bar{D}B\gamma$ decay threshold, current uncertainties do not allow us to
determine whether such a state would decay electromagnetically, or only weakly.
We also perform a study at fixed pion mass, with NRQCD for the heavy quarks,
simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime
\bar{b}^\prime\bar{b}^\prime$ tetraquarks with $q,\, q^\prime =ud$ or $\ell s$
and variable, unphysical $m_{b^\prime}$ in order to investigate the heavy
mass-dependence of such tetraquark states. We find that the dependence of the
binding energy follows a phenomenologically-expected form and that, though
NRQCD breaks down before $m_{b^\prime}=m_c$ is reached, the results at higher
$m_{b^\prime}$ clearly identify the $ud\bar{b}^\prime \bar{b}$ channel as the
most likely to support a strong-interaction-stable tetraquark state at
$m_{b^\prime}=m_c$. This observation serves to motivate the direct
$ud\bar{c}\bar{b}$ simulation. Throughout we use dynamical $n_f=2+1$ ensembles
with pion masses $m_\pi=$415, 299, and 164 MeV reaching down almost to the
physical point, a relativistic heavy quark prescription for the charm quark,
and NRQCD for the bottom quark(s).
