The CRESST-III experiment which is dedicated to low-mass dark matter search uses scintillating CaWO$_4$ crystals operated as cryogenic particle detectors. Background discrimination is achieved by exploiting the scintillating light signal of CaWO$_4$ and by a novel active detector holder presented in this paper. In a test setup above ground, a nuclear-recoil energy threshold of $E_{th}=(190.6pm5.2)$eV is reached with a 24g prototype detector, which corresponds to an estimated threshold of $sim$50eV when being operated in the low-noise CRESST cryostat. This is the lowest threshold reported for direct dark matter searches. For CRESST-III phase 1, ten such detector modules were installed in the cryostat which have the potential to improve significantly the sensitivity to scatterings of dark matter particles with masses down to $sim$0.1GeV/c$^2$.
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