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The NEMO-3 detector, which had been operating in the Modane UndergroundLaboratory from 2003 to 2010, was designed to search for neutrinoless double$\beta$ ($0\nu\beta\beta$) decay. We report final results of a search for$0\nu\beta\beta$ decays with $6.914$ kg of $^{100}$Mo using the entire NEMO-3data set with a detector live time of $4.96$ yr, which corresponds to anexposure of 34.3 kg$\cdot$yr. We perform a detailed study of the expectedbackground in the $0\nu\beta\beta$ signal region and find no evidence of$0\nu\beta\beta$ decays in the data. The level of observed background in the$0\nu\beta\beta$ signal region $[2.8-3.2]$ MeV is $0.44 \pm 0.13$ counts/yr/kg,and no events are observed in the interval $[3.2-10]$ MeV. We therefore derivea lower limit on the half-life of $0\nu\beta\beta$ decays in $^{100}$Mo of$T_{1/2}(0\nu\beta\beta)> 1.1 \times 10^{24}$ yr at the $90\%$ ConfidenceLevel, under the hypothesis of light Majorana neutrino exchange. Depending onthe model used for calculating nuclear matrix elements, the limit for theeffective Majorana neutrino mass lies in the range $\langle m_{\nu} \rangle <0.33$--$0.62$ eV. We also report constraints on other lepton-number violatingmechanisms for $0\nu\beta\beta$ decays.

Result of the search for neutrinoless double-$\beta$ decay in $^{100}$Mo with the NEMO-3 experiment