Covalent organic frameworks (COFs) are a class of advanced nanoporous polymeric materials which combine the crystallinity of metalorganic frameworks (MOFs) with the stability and potentially low-cost organic chemistry of porous polymer networks (PPNs). Like other advanced porous materials, COFs can potentially be designed to meet the needs of a variety of applications, from energy, to security, to human health. In this work, we construct in silico a database of hypothetical three-dimensional, crystalline COFs. In constructing this library we generate novel COFs using only established synthetic routes, previously utilized tetrahedral building units, and commercially available bridging linker molecules. This ensures that there are no known chemical barriers to synthesizing all materials in our database. We relaxed all materials in our database through semiempirical electronic structure calculations. In addition, for those structures that allow interpenetration, we designed interpenetrated versions of the basic structure. Then, we characterized the porosity of each of these structures. The final set of 4147 structures (based on 620 unique noninterpenetrated structures) and their computed properties are publicly available and can be screened to identify promising materials for a wide variety of applications. Here, we assess the suitability of our COFs for vehicular methane storage by performing molecular simulations to predict the equilibrium methane uptake.