  We perform a deep survey of planetary nebulae (PNe) in the spiral galaxy NGC
300 to construct its planetary nebula luminosity function (PNLF). We aim to
derive the distance using the PNLF and to probe the characteristics of the most
luminous PNe. We analyse 44 fields observed with MUSE at the VLT, covering a
total area of $\sim11$ kpc$^2$. We find [OIII]5007 sources using the
differential emission line filter (DELF) technique. We identify PNe through
spectral classification using the aid of the BPT-diagram. The PNLF distance is
derived using the maximum likelihood estimation technique. For the more
luminous PNe, we also measure their extinction using the Balmer decrement. We
estimate the luminosity and effective temperature of the central stars of the
luminous PNe, based on estimates of the excitation class and the assumption of
optically thick nebulae. We identify 107 PNe and derive a most-likely distance
modulus $(m-M)_0 = 26.48^{+0.11}_{-0.26}$ ($d = 1.98^{+0.10}_{-0.23}$ Mpc). We
find that the PNe at the PNLF cut-off exhibit relatively low extinction, with
some high extinction cases caused by local dust lanes. We present the lower
limit luminosities and effective temperatures of the central stars for some of
the brighter PNe. We also identify a few Type I PNe that come from a young
population with progenitor masses $>2.5 \, M_\odot$, however do not populate
the PNLF cut-off. The spatial resolution and spectral information of MUSE allow
precise PN classification and photometry. These capabilities also enable us to
resolve possible contamination by diffuse gas and dust, improving the accuracy
of the PNLF distance to NGC 300.
