We develop a 16-band k center dot p model for the description of wurtzite GaAs, together with a scheme to determine electronic structure parameters for multiband k center dot p models. Our approach uses low-discrepancy sequences to fit k center dot p band structures beyond the eight-band scheme to most recent ab initio data, obtained within the framework for hybrid-functional density functional theory with a screened-exchange hybrid functional. We report structural parameters, elastic constants, band structures along high-symmetry lines, and deformation potentials at the Gamma point. Based on this, we compute the bulk electronic properties (Gamma point energies, effective masses, Luttinger-like parameters, and optical matrix parameters) for a ten-band and a sixteen-band k center dot p model for wurtzite GaAs. Our fitting scheme can assign priorities to both selected bands and k points that are of particular interest for specific applications. Finally, ellipticity conditions can be taken into account within our fitting scheme in order to make the resulting parameter sets robust against spurious solutions.