This paper reports details of our record-breaking computations on lattice problems, including the Shortest Vector Problem (SVP), Learning With Errors (LWE), and NTRU challenges. The results were obtained using successive bucket sieving (Becker–Gama–Joux 2015) implemented on a GPU-enabled, heterogeneous memory architecture. Our method achieves lower computational complexity and reduced memory demands compared to all existing work, while scaling to massive parallelism. In particular, we are able to place the hundred-terabyte sieving data on disk without disk I/O becoming a bottleneck. And our work points out a clear path to solve SVP 260 with reasonable cost in a reasonable time frame (1 year). We also compare the practical quality of BGJ and BDGL (Becker–Ducas–Gama–Laarhoven 2016) bucketing, and evaluate the effect of quantization on lattice sieving. It turns out that even in a pure algorithmic setting, the advantage of BDGL over BGJ is minor and grows tamely with the sieving rank. This work suggests that lattice attacks remain rapidly advancing, and that large-scale sieving may be less memory-bound than commonly assumed. Consequently, we recommend conservative parameter choices when migrating to lattice-based post-quantum cryptography.