We report constraints on spin-independent weakly interacting massive particle (WIMP)-nucleon scattering using a 3.35e4 kg-day exposure of the Large Underground Xenon (LUX) experiment. A dual-phase xenon time projection chamber with 250 kg of active mass is operated at the Sanford Underground Research Facility under Lead, South Dakota (USA). With roughly four-fold improvement in sensitivity for high WIMP masses relative to our previous results, this search yields no evidence of WIMP nuclear recoils. At a WIMP mass of 50 GeV/c^2, WIMP-nucleon spin-independent cross sections above 2.2e-46 cm^2 are excluded at the 90% confidence level.
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