The Materials Genome is in action: the molecular codes for millions of materials have been sequenced, predictive models have been developed, and now the challenge of hydrogen storage is targeted. Renewably generated hydrogen is an attractive transportation fuel with zero carbon emissions, but its storage remains a significant challenge. Nanoporous adsorbents have shown promising physical adsorption of hydrogen approaching targeted capacities, but the scope of studies has remained limited. Here the Nanoporous Materials Genome, containing over 850 000 materials, is analyzed with a variety of computational tools to explore the limits of hydrogen storage. Optimal features that maximize net capacity at room temperature include pore sizes of around 6 Å and void fractions of 0.1, while at cryogenic temperatures pore sizes of 10 Å and void fractions of 0.5 are optimal. Our top candidates are found to be commercially attractive as "cryo-adsorbents", with promising storage capacities at 77 K and 100 bar with 30% enhancement to 40 g/L, a promising alternative to liquefaction at 20 K and compression at 700 bar.