  Reverberation mapping measurements have been used to constrain the
relationship between the size of the broad-line region and luminosity of active
galactic nuclei (AGN). This $R-L$ relation is used to estimate single-epoch
virial black hole masses, and has been proposed for use to standardise AGN to
determine cosmological distances. We present reverberation measurements made
with H$\beta$ from the six-year Australian Dark Energy Survey (OzDES)
Reverberation Mapping Program. We successfully recover reverberation lags for
eight AGN at $0.12<z< 0.71$, probing higher redshifts than the bulk of H$\beta$
measurements made to date. Our fit to the $R-L$ relation has a slope of
$\alpha=0.41\pm0.03$ and an intrinsic scatter of $\sigma=0.23\pm0.02$ dex. The
results from our multi-object spectroscopic survey are consistent with previous
measurements made by dedicated source-by-source campaigns, and with the
observed dependence on accretion rate. Future surveys, including LSST, TiDES
and SDSS-V, which will be revisiting some of our observed fields, will be able
to build on the results of our first-generation multi-object reverberation
mapping survey.
