  We use lattice QCD to investigate the existence of strong-interaction-stable
antiheavy-antiheavy-light-light tetraquarks. We study the $\bar b \bar b u s$
system with quantum numbers $J^P = 1^+$ as well as the $\bar b \bar c u d$
systems with quantum numbers $I(J^P) = 0(0^+)$ and $I(J^P) = 0(1^+)$. We carry
out computations on five gauge-link ensembles with $2 + 1$ flavors of
domain-wall fermions, including one at the physical pion mass. The bottom
quarks are implemented using lattice nonrelativistic QCD, and the charm quarks
using an anisotropic clover action. In addition to local diquark-antidiquark
and local meson-meson interpolating operators, we include nonlocal meson-meson
operators at the sink, which facilitates the reliable determination of the
low-lying energy levels. We find clear evidence for the existence of a
strong-interaction-stable $\bar b \bar b u s$ tetraquark with binding energy
$(-86 \pm 22 \pm 10) \, \text{MeV}$ and mass $(10609 \pm 22 \pm 10) \,
\text{MeV}$. For the $\bar b \bar c u d$ systems we do not find any indication
for the existence of bound states, but cannot rule out their existence either.
