Abstract: Approximate nearest-neighbor search on GPUs serves retrieval-augmented generation, recommendation, and deduplication over datasets of up to billions of vectors. The fastest GPU indexes at high recall, such as CAGRA, walk proximity graphs in chained rounds, each of which waits for the distances of the previous one. High recall therefore costs many dependent rounds per query. Our insight is to spend the HBM of the GPUs on precomputed neighbor lists, so that a query reads its candidates in one parallel step instead of a chain of rounds. This paper turns the above insight into a GPU vector search system, namely OctEx, which holds hundreds of randomly projected copies of the dataset in GPU memory. Every copy rounds its vectors to the nearest points of a regular grid whose cells are nearly round and stores for every populated cell the list of vectors nearest to its center. A query reads the lists of its cells in all copies at once and then, in a fixed number of waves, the precomputed neighbor lists of its best hits. OctEx ranks the union of all hits by an int8 sketch before one exact rerank. OctEx runs the whole search of a batch as CUDA graphs over all GPUs of a server and places every part of its index in HBM or host memory by its access frequency. On four H100 GPUs at recall 0.95 to 0.995, OctEx outperforms CAGRA by 2.0x to 46.4x on seven datasets of up to one hundred million vectors, and by 1.46x to 2.05x on the one billion vectors of Deep1B and SIFT1B, whose indexes it builds in 44 to 47 minutes. OctEx also outperforms GGNN, PathWeaver, FlowANN, and the cuVS inverted file indexes IVF-PQ and IVF-RaBitQ by 5.4x to 343x.