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Abstract Hot DA white dwarfs (DAWDs) have fully radiative pure hydrogen atmospheres that are the least complicated to model. Pulsationally stable, they are fully characterized by their effective temperatureT_effand surface gravity $\log g$, which can be deduced from their optical spectra and used in model atmospheres to predict their spectral energy distributions (SEDs). Based on this, three bright DAWDs have defined the spectrophotometric flux scale of the CALSPEC system of the Hubble Space Telescope (HST). In this paper we add 32 new fainter (16.5 <V< 19.5) DAWDs spread over the whole sky and within the dynamic range of large telescopes. Using ground-based spectra and panchromatic photometry with HST/WFC3, a new hierarchical analysis process demonstrates consistency between model and observed fluxes above the terrestrial atmosphere to <0.004 mag rms from 2700 to 7750 Å and to 0.008 mag rms at 1.6μm for the total set of 35 DAWDs. These DAWDs are thus established as spectrophotometric standards with unprecedented accuracy from the near-ultraviolet to the near-infrared, suitable for both ground- and space-based observatories. They are embedded in existing surveys like the Sloan Digital Sky Survey, Pan-STARRS, and Gaia, and will be naturally included in the Large Synoptic Survey Telescope  survey by the Rubin Observatory. With additional data and analysis to extend the validity of their SEDs further into the infrared, these spectrophotometric standard stars could be used for JWST, as well as for the Roman and Euclid observatories.