  A new upper limit on the 21-cm signal power spectrum at a redshift of $z
\approx 9.1$ is presented, based on 141 hours of data obtained with the
Low-Frequency Array (LOFAR). The analysis includes significant improvements in
spectrally-smooth gain-calibration, Gaussian Process Regression (GPR)
foreground mitigation and optimally-weighted power spectrum inference.
Previously seen `excess power' due to spectral structure in the gain solutions
has markedly reduced but some excess power still remains with a spectral
correlation distinct from thermal noise. This excess has a spectral coherence
scale of $0.25 - 0.45$\,MHz and is partially correlated between nights,
especially in the foreground wedge region. The correlation is stronger between
nights covering similar local sidereal times. A best 2-$\sigma$ upper limit of
$\Delta^2_{21} < (73)^2\,\mathrm{mK^2}$ at $k = 0.075\,\mathrm{h\,cMpc^{-1}}$
is found, an improvement by a factor $\approx 8$ in power compared to the
previously reported upper limit. The remaining excess power could be due to
residual foreground emission from sources or diffuse emission far away from the
phase centre, polarization leakage, chromatic calibration errors, ionosphere,
or low-level radio-frequency interference. We discuss future improvements to
the signal processing chain that can further reduce or even eliminate these
causes of excess power.
