Authors: Jaeuk Kim and Salvatore Torquato\\ Disordered hyperuniform packings (or dispersions) are unusual amorphous states of two-phase materials that are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in disordered hyperuniform materials, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a “bounded-cell” condition, hard particles are placed inside each cell such that the volume fraction of this cell occupied with these particles becomes identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit. We numerically implement this procedure to two distinct types of initial tessellations; Voronoi and sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in two and three dimensions. Application to sphere tessellations establishes the hyperuniformity of the classical Hashin-Shtrikman coated-spheres structures that possess optimal effective transport and elastic properties.