2026-07-22T11:26:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23228 2025-10-02T12:43:40Z ddc:004 open_access

A Note on the No-(d+2)-On-a-Sphere Problem Suk, Andrew White, Ethan Patrick General position no-four-on-a-cirle d-dimensional lattice cube For fixed d ≥ 3, we construct subsets of the d-dimensional lattice cube [n]^d of size n^{3/(d + 1) - o(1)} with no d+2 points on a sphere or a hyperplane. This improves the previously best known bound of Ω(n^{1/(d-1)}) due to Thiele from 1995. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrew Suk and Ethan Patrick White 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.76 urn:nbn:de:0030-drops-232287 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.76 eng https://creativecommons.org/licenses/by/4.0/legalcode