  Fluctuations play a key role in the study of QCD phases. Lattice QCD is a
valuable tool to calculate them, but going to high orders is challenging. Up to
the fourth order, continuum results are available since 2015. We present the
first continuum results for sixth order baryon fluctuations for temperatures
between $T=130 - 200$ MeV, and eighth order at $T=145$ MeV in a fixed volume.
We show that for $T \leq 145$ MeV, relevant for criticality search, finite
volume effects are under control. Our results are in sharp contrast with well
known results in the literature obtained at finite lattice spacing.
