Estimates of the cosmic gamma-ray flux at PeV to EeV energies from the EAS-MSU experiment data

Archival EAS–MSU data are searched for anomalous muonless events which may be caused by primary gamma rays with energies between $10^{15}$ and $10^{18}$ eV. We consider a refined sample of high-quality data and confirm the previously reported detection of a non-zero gamma-ray flux at $\sim5\cdot10^{16}$ eV with a similar flux value but at somewhat lower statistical significance, corresponding to a depletion of the sample. We present upper limits on the flux below and above these energies, including the first constraints in the range $10^{16.5}{-}10^{17.5}$ eV never studied by any other experiment.