A new MWA limit on the 21 cm Power Spectrum at Redshifts $\sim$ 13 $-$
  17
  Observations in the lowest MWA band between $75-100$ MHz have the potential
to constrain the distribution of neutral hydrogen in the intergalactic medium
at redshift $\sim 13-17$. Using 15 hours of MWA data, we analyse systematics in
this band such as radio-frequency interference (RFI), ionospheric and wide
field effects. By updating the position of point sources, we mitigate the
direction independent calibration error due to ionospheric offsets. Our
calibration strategy is optimized for the lowest frequency bands by reducing
the number of direction dependent calibrators and taking into account radio
sources within a wider field of view. We remove data polluted by systematics
based on the RFI occupancy and ionospheric conditions, finally selecting 5.5
hours of the cleanest data. Using these data, we obtain two sigma upper limits
on the 21 cm power spectrum in the range of $0.1\lessapprox k \lessapprox 1
~\rm ~h~Mpc^{-1}$ and at $z$=14.2, 15.2 and 16.5, with the lowest limit being
$6.3\times 10^6 ~\rm mK^2$ at $\rm k=0.14 \rm ~h~Mpc^{-1}$ and at $z=15.2$ with
a possibility of a few \% of signal loss due to direction independent
calibration.
