Test of Neutrino Oscillations Using Atmospheric Neutrinos

We study the distributions of 135 atmospheric neutrino events collected in 420 days of running in a large, deep underground detector. These events come from neutrinos with path lengths ranging from a few kilometers to over ${10}^{4}$ kilometers. The average neutrino energy is 920 MeV. No evidence for neutrino oscillations is observed. Flux-independent limits for $\ensuremath{\Delta}{m}_{\ensuremath{\nu}}^{2}$ in the range of 2.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ to 11.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ e${\mathrm{V}}^{2}$ are set for maximum mixing.