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This improves the bound $\\Omega(n\\log n)$ of Edelsbrunner, Valtr and Welzl from 1997.\n  Our construction can be generalized to higher dimensions, for any $d$ we construct a dense point set of $n$ points in $\\mathbb{R}^d$ with $n^{d-1}e^{\\Omega\\left({\\sqrt{\\log n}}\\right)}$ halving hyperplanes. 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