  Motivated by multiple phenomenological considerations, we perform the first
search for the existence of a $\bar{b}\bar{b}bb$ tetraquark bound state with a
mass below the lowest non-interacting bottomonium-pair threshold using the
first-principles lattice non-relativistic QCD methodology. We use a full
$S$-wave colour/spin basis for the $\bar{b}\bar{b}bb$ operators in the three
$0^{++}$, $1^{+-}$ and $2^{++}$ channels. We employ four gluon field ensembles
at multiple lattice spacing values ranging from $a = 0.06 - 0.12$ fm, all of
which include $u$, $d$, $s$ and $c$ quarks in the sea, and one ensemble which
has physical light-quark masses. Additionally, we perform novel exploratory
work with the objective of highlighting any signal of a near threshold
tetraquark, if it existed, by adding an auxiliary potential into the QCD
interactions. With our results we find no evidence of a QCD bound tetraquark
below the lowest non-interacting thresholds in the channels studied.
