A new approach for direct third-harmonic generation is the generation inside a stack of dielectric layers. At present, our highest conversion efficiency achieved is 3.5\%. This contribution provides an overview of the design process, production, measurement results, and their agreement with simulation results. To create the frequency tripling mirror designs, we use a combination of a Monte Carlo algorithm and a Meep-based algorithm to solve Maxwell's equations. Mandatory for the production of the mirrors is a very precise knowledge of the dispersion data of the materials used. For this purpose, the dispersion data of the coating materials are re-fitted using in-situ transmission data of a BBM after each coating run. In combination with various measures to maintain a stable refractive index of the used Hf_xAl_yO, high coating thickness accuracies are achieved in this way. Finally, experimental measurements and simulation results are compared using the post-fitted dispersion and layer thickness data.