  A search for the doubly heavy $\mathit{\Xi}_{bc}^{0}$ baryon using its decay
to the $D^0pK^-$ final state is performed using proton-proton collision data at
a centre-of-mass energy of 13 TeV collected by the LHCb experiment between 2016
and 2018, corresponding to an integrated luminosity of 5.4 $\mathrm{fb}^{-1}$.
No significant signal is found in the invariant mass range from 6.7 to 7.2
$\mathrm{GeV}/c^2$. Upper limits are set at $95\%$ credibility level on the
ratio of the $\mathit{\Xi}_{bc}^{0}$ production cross-section times its
branching fraction to $D^0pK^-$ relative to that of the
$\mathit{\Lambda}_{b}^{0} \to D^0pK^-$ decay. The limits are set as a function
of the $\mathit{\Xi}_{bc}^{0}$ mass and lifetime hypotheses, in the rapidity
range from 2.0 to 4.5 and in the transverse momentum region from 5 to 25
$\mathrm{GeV}/c$. Upper limits range from $1.7\times10^{-2}$ to
$3.0\times10^{-1}$ for the considered $\mathit{\Xi}_{bc}^{0}$ mass and lifetime
hypotheses.
