A major challenge in reinforcement learning is to develop practical, sample-efficient algorithms for exploration in high-dimensional domains where generalization and function approximation is tequired. Low-Rank Markov Decision Processes—where transition probabilities admit a low-rank factorization based on an unknown feature embedding—offer a simple, yet expressive framework for RL with function approximation, but existing algorithms are either (1) computationally intractable, or (2) reliant upon restrictive statistical assumptions such as latent variable structure, access to model-based function approximation, or reachability. In this work, we propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs that is both computationally efficient and model-free, allowing for general function approximation and requiring no additional structural assumptions. Our algorithm, VoX, uses the notion of a generalized optimal design for the feature embedding as an efficiently computable basis for exploration, performing efficient optimal design computation by interleaving representation learning and policy optimization. Our analysis—which is appealingly simple and modular—carefully combines several techniques, including a new reduction from optimal design computation to policy optimization based on the Frank-Wolfe method, and an improved analysis of a certain minimax representation learning objective found in prior work.