Next-generation extreme ultraviolet (EUV) systems with numerical apertures of 0.55 have the potential to provide sub-8-nm half-pitch resolution. The increased importance of stochastic effects at smaller feature sizes places further demands on scanner and mask to provide high contrast images. We use rigorous mask diffraction and imaging simulation to understand the impact of the EUV mask absorber and to identify the most appropriate optical parameters for high NA EUV imaging. Simulations of various use cases and material options indicate two main types of solutions: high extinction materials, especially for lines spaces, and low refractive index materials that can provide phase shift mask solutions. EUV phase masks behave very different from phase shift masks for DUV. Carefully designed low refractive index materials and masks can open up a new path toward high contrast edge printing.