We report results of a search for oscillations involving a light sterile neutrino over distances of 1.04 and $735,mathrm{km}$ in a $ u_{mu}$-dominated beam with a peak energy of $3,mathrm{GeV}$. The data, from an exposure of $10.56times 10^{20},textrm{protons on target}$, are analyzed using a phenomenological model with one sterile neutrino. We constrain the mixing parameters $theta_{24}$ and $Delta m^{2}_{41}$ and set limits on parameters of the four-dimensional Pontecorvo-Maki-Nakagawa-Sakata matrix, $|U_{mu 4}|^{2}$ and $|U_{tau 4}|^{2}$, under the assumption that mixing between $ u_{e}$ and $ u_{s}$ is negligible ($|U_{e4}|^{2}=0$). No evidence for $ u_{mu} to u_{s}$ transitions is found and we set a world-leading limit on $theta_{24}$ for values of $Delta m^{2}_{41} lesssim 1,mathrm{eV}^{2}$.
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