Bezdek, Károly; Blokhuis, Aart The Radon number of the three-dimensional integer lattice. (English) Zbl 1043.52010 Discrete Comput. Geom. 30, No. 2, 181-184 (2003). S. Onn [SIAM J. Discrete Math. 4, No. 3, 436–447 (1991; Zbl 0735.52007)] proved that the Radon number \(r(d)\) of the \(d\)-dimensional integer lattice fulfills the inequalities \(5\cdot 2 ^{d-2} +1 \leq r(d) \leq d(2^ d -1) +3\). So in particular, \(11 \leq r(3) \leq 24\). The authors of the present note improve the right inequality up to \(r(3) \leq 17\). Reviewer: Marek Lassak (Bydgoszcz) Cited in 3 Documents MSC: 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 68Q25 Analysis of algorithms and problem complexity 52A35 Helly-type theorems and geometric transversal theory Keywords:integer lattice; Radon number; Radon partition Citations:Zbl 0735.52007 PDFBibTeX XMLCite \textit{K. Bezdek} and \textit{A. Blokhuis}, Discrete Comput. Geom. 30, No. 2, 181--184 (2003; Zbl 1043.52010)