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In the absence of time-reversal invariance, metals without inversion symmetrymay exhibit nonreciprocal charge transport -- a magnetochiral anisotropy thatmanifests as unequal electrical resistance for opposite current flowdirections. If superconductivity also sets in, the charge transmission maybecome dissipationless in one direction while remaining dissipative in theopposite, thereby realizing a superconducting diode. Through bothdirect-current and alternating-current measurements, we study the nonreciprocaleffects in thin films of the noncentrosymmetric superconductorT$_d$-MoTe\textsubscript{2} with disorders. We observe nonreciprocalsuperconducting critical currents with a diode efficiency close to 20\%~, and alarge magnetochiral anisotropy coefficient up to$\SI{5.9e8}{\per\tesla\per\ampere}$, under weak out-of-plane magnetic field inthe millitesla range. The great enhancement of rectification efficiency underout-of-plane magnetic field is likely abscribed to the vortex ratchet effect,which naturally appears in the noncentrosymmetric superconductor withdisorders. Intriguingly, unlike the finding in Rashba systems, the strongestin-plane nonreciprocal effect does not occur when the field is perpendicular tothe current flow direction. We develop a phenomenological theory to demonstratethat this peculiar behavior can be attributed to the asymmetric structure ofspin-orbit coupling in T$_d$-MoTe\textsubscript{2}. Our study highlights howthe crystallographic symmetry critically impacts the nonreciprocal transport,and would further advance the research for designing the superconducting diodewith the best performance.

Superconducting Diode Effect and Large Magnetochiral Anisotropy in T$_d$-MoTe$_2$ Thin Film