Current Status of the Dark Matter Search Experiment CRESST

CRESST is a cryogenic direct Dark Matter search experiment based on phonon-lighttechnique. It is aiming for the detection of \textit{weakly interacting massiveparticles} (WIMPs) via their scattering off nuclei in $\mathrm{CaWO_4}${} targetcrystals. Significant improvements have been achieved with respect to previousmeasurement campaigns in terms of intrinsic radiopurity of $\mathrm{CaWO_4}${} crystals andrejection of nuclear recoil events from alpha decays near surfaces. In thiscontribution, the related changes in the detector design will be discussed.Based on the first $\sim 30$\,kg-live-days of data acquired by a single $\mathrm{CaWO_4}${} detector modulewith a new design, we present limits for the spin-independent WIMP-nucleoncross section, which exclude new parameter space below $3\,\mathrm{GeV}/c^2$