  We investigate the `Local Hole', an anomalous under-density in the local
galaxy environment, by extending our previous galaxy $K-$band number-redshift
and number-magnitude counts to $\approx 90\%$ of the sky. Our redshift samples
are taken from the 2MASS Redshift Survey (2MRS) and the 2M++ catalogues,
limited to $K<11.5$. We find that both surveys are in good agreement, showing
an $\approx 21-22\%$ under-density at $z<0.075$ when compared to our
homogeneous counts model that assumes the same luminosity function and other
parameters as in our earlier papers. Using the Two Micron All Sky Survey
(2MASS) for $n(K)$ galaxy counts, we measure an under-density relative to this
model of $20\pm 2 \%$ at $K<11.5$, which is consistent in both form and scale
with the observed $n(z)$ under-density. To examine further the accuracy of the
counts model, we compare its prediction for the fainter $n(K)$ counts of the
Galaxy and Mass Assembly (GAMA) survey. We further compare these data with a
model assuming the parameters of a previous study where little evidence for the
Local Hole was found. At $13<K<16$ we find a significantly better fit for our
model, arguing for our higher luminosity function normalisation. Although our
implied under-density of $\approx 20\%$ means local measurements of the Hubble
Constant have been over-estimated by $\approx3$\%, such a scale of
under-density is in tension with a global $\Lambda$CDM cosmology at an
$\approx3\sigma$ level.
