  Recently two collaborations, Tibet and HAWC, presented new measurements of
gamma-ray spectrum from Crab Nebula
\cite{Amenomori:2019rjd},\cite{Abeysekara:2019edl} which continues beyond $100$
TeV. We use these data to establish two-sided constraints on parameters of
Lorentz Invariance violation in quantum electrodynamics. The limits on Lorentz
violating mass scale for quartic dispersion relation are $4.1\times 10^{14}\
\mbox{GeV}$ (photon splitting) and $1.9\times 10^{13}\ \mbox{GeV}$ (photon
decay) for superluminal case, and $1.4\times 10^{12}$ GeV (suppression of
shower formation) for subluminal case.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology