  We study the LHC discovery potential of the double-bottom tetraquarks $bb
\bar u \bar d$, $bb \bar u \bar s$ and $bb \bar d \bar s$, the lightest of
which having $J^P=1^+$, called $T^{\{bb\}}_{[\bar u \bar d]}$,
$T^{\{bb\}}_{[\bar u \bar s]}$ and $T^{\{bb\}}_{[\bar d \bar s]}$, are expected
to be stable against strong decays. Employing the Monte Carlo generators
MadGraph5$\_$aMC@NLO and Pythia6, we simulate the process $pp\to \bar b b\bar b
b$ and calculate the $b b$-diquark jet configurations, specified by the
invariant mass interval $m_{bb} < M_{T^{\{bb\}}_{[\bar q \bar q']}} + \Delta
M$. Estimates of $\Delta M$ from the measured product $\sigma(pp \to B_c^+
+X){\cal B}(B_c^+\to J/\psi\pi^+)$ are presented and used to to get the $b
b$-diquark jet cross sections in double-bottom hadrons $\sigma(pp \to
H_{\{bb\}} +X)$, where $H_{\{bb\}} $ represent tetraquarks and baryons. This is
combined with the LHCb data on the fragmentation $b \to \Lambda_b$ and $b \to
B$ to obtain $\sigma(pp\to T^{\{bb\}}_{[\bar u\bar d]} +X) = (2.4
^{+0.9}_{-0.6})\ \text{nb} $, and about a half of this for the
$T^{\{bb\}}_{[\bar{u}\bar{s}]}$ and $T^{\{bb\}}_{[\bar d \bar s]}$. We also
present estimates of the production cross sections for the mixed bottom-charm
tetraquarks, $bc \bar u \bar d$, $bc \bar u \bar s$ and $bc \bar d \bar s$,
obtaining $\sigma(pp\to T^{[bc]}_{[\bar u \bar d]} +X)= (48^{+19}_{-12})\ {\rm
nb}$, and the related ones having $T^{[bc]}_{[\bar u \bar s]}$ and
$T^{[bc]}_{[\bar d \bar s]}$. They have excellent discovery potential at the
LHC, as their branching ratios in various charge combinations of $BD_{(s)}
(\gamma)$ are anticipated to be large.
