{"id":"palomar/PALOMAR-2026-09-05-000004","url":"https://github.com/lennrt/palomar-formalizations/tree/cc754a3bd42b2c0be28ff0a9e87c6d71e2fbfd82/zenodo-21925582/palomar","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-05-000004-v1.json","repo":"https://github.com/lennrt/palomar-formalizations","tags":["math.NA","cs.NA","msc:11K38","msc:11K45","msc:65C05","msc:65D30","quasi-monte-carlo","sobol-sequences","digital-nets"],"score":0,"title":"Exact four-dimensional projection quality of the OneTwo Sobol' table at 65,536 points","trust":"high","domain":"math.NA","source":"palomar","authors":["Lennart Rudolph"],"reviews":0,"subject":"math.NA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-05","reactions":{},"formalized":true,"formalizes":[{"title":"Exact Projection Quality of OneTwo Sobol' Sequences at 65,536 Points","identifier":"doi:10.5281/zenodo.21925582","relationship":"formalizes"}]}