Open Research Index

Exact four-dimensional projection quality of the OneTwo Sobol' table at 65,536 points

Lennart Rudolph

Palomar Registrypalomar/PALOMAR-2026-09-05-000004Sep 5, 2026math.NAscore 0

The quality parameter t of a base-2 digital net with 2^m points measures exact equidistribution in dyadic boxes, and for Sobol' sequences used in quasi-Monte Carlo integration and computer graphics the quality of low-dimensional projections is a practical bottleneck. The OneTwo construction of Bonneel, Coeurjolly, Iehl, and Ostromoukhov (ACM Transactions on Graphics, 2025) releases a 692-dimension direction-number table whose protected pairs (2k-1, 2k) have the (1,2) property, with acceptance targets t <= 3 through m <= 10 and t <= 4 through m <= 15 for the pair-aligned four-dimensional…

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