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  1. ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Aichholzer, Oswin; Wang, Haitao (Ed.)
    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. 
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    Free, publicly-accessible full text available January 1, 2026