  Aims: We aim to measure the Crab Nebula gamma-ray spectral energy
distribution in the ~100 TeV energy domain and test the validity of existing
leptonic emission models at these high energies.
  Methods: We use the novel very large zenith angle observations with the MAGIC
telescope system to increase the collection area above 10 TeV. We also develop
an auxiliary procedure of monitoring atmospheric transmission in order to
assure proper calibration of the accumulated data. This employs recording of
optical images of the stellar field next to the source position, which provides
a better than 10% accuracy for the transmission measurements.
  Results: We demonstrate that MAGIC very large zenith angle observations yield
a collection area larger than a square kilometer. In only ~56 hr of
observations, we detect the gamma-ray emission from the Crab Nebula up to 100
TeV, thus providing the highest energy measurement of this source to date with
Imaging Atmospheric Cherenkov Telescopes. Comparing accumulated and archival
MAGIC and Fermi/LAT data with some of the existing emission models, we find
that none of them provides an accurate description of the 1 GeV to 100 TeV
gamma-ray signal.
