  We present a public catalogue of numerical-relativity binary-black-hole
simulations. The catalogue contains datasets from 80 distinct configurations of
precessing binary-black-hole systems, with mass ratios up to $m_2/m_1 = 8$,
dimensionless spin magnitudes on the larger black hole up to $|\vec{S}_2|/m_2^2
= 0.8$ (the small black hole is non-spinning), and a range of five values of
spin misalignment for each mass-ratio/spin combination. We discuss the physical
properties of the configurations in our catalogue, and assess the accuracy of
the initial configuration of each simulation and of the gravitational
waveforms. We perform a careful analysis of the errors due to the finite
resolution of our simulations and the finite distance from the source at which
we extract the waveform data and provide a conservative estimate of the
mismatch accuracy. We find that the upper limit on the mismatch uncertainty of
our waveforms is $0.4\%$. In doing this we present a consistent approach to
combining mismatch uncertainties from multiple error sources. We compare this
release to previous catalogues and discuss how these new simulations complement
the existing public datasets. In particular, this is the first catalogue to
uniformly cover this parameter space of single-spin binaries and there was
previously only sparse coverage of the precessing-binary parameter space for
mass ratios $\gtrsim 5$. We discuss applications of these new data, and the
most urgent directions for future simulation work. The public dataset can be
accessed online at https://data.cardiffgravity.org/bam-catalogue/.
