In an effort to help constrain the origins of gamma-ray bursts, we have searched data from the CYGNUS experiment for evidence of gamma-ray burst radiation higher than previously detected. By monitoring the single-particle rates from photomultiplier tubes in the five CYGNUS water-Cerenkov detectors, we have placed upper limits on the flux of radiation {dollar}sbsp{lcub}sim{rcub}{lcub}>{rcub}{dollar}100 GeV coincident with 9 recent strong gamma-ray bursts. Using reconstructed events from the CYGNUS-I array we searched for coincident or longer-lasting emission of ultra-high-energy radiation ({dollar}sbsp{lcub}sim{rcub}{lcub}>{rcub}{dollar}50 TeV) from 469 gamma-ray bursts listed in the third BATSE catalog or elsewhere. No statistically significant excess was found for the bursts on any of the timescales searched. The ultra-high-energy flux upper limits for three of the bursts imply either a softening of the production spectrum between 2 MeV and {dollar}sim{dollar}20 TeV, or the presence of ultra-high-energy gamma-ray absorption by intergalactic radiation fields. If the production spectrum does not soften, the bursts must have a cosmological origin. |