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Improved dispersion bounds for modified Fibonacci lattices
Journal of Complexity ( IF 1.8 ) Pub Date : 2020-10-06 , DOI: 10.1016/j.jco.2020.101522 Ralph Kritzinger , Jaspar Wiart
中文翻译:
改进的斐波那契晶格的改进色散界
更新日期:2020-10-06
Journal of Complexity ( IF 1.8 ) Pub Date : 2020-10-06 , DOI: 10.1016/j.jco.2020.101522 Ralph Kritzinger , Jaspar Wiart
We study the dispersion of point sets in the unit square; i.e. the size of the largest axes-parallel box amidst such point sets. It is known that where is the minimal possible dispersion for an -element point set in the unit square. The upper bound 2 is obtained by an explicit point construction—the well-known Fibonacci lattice. In this paper we find a modification of this point set such that its dispersion is significantly lower than the dispersion of the Fibonacci lattice. Our main result will imply that
中文翻译:
改进的斐波那契晶格的改进色散界
我们研究点集在单位平方中的离散度;即,在这些点集中的最大平行轴框的大小。众所周知 哪里 是对于 -在单位正方形中设置的元素点。上限2是通过显式点构造-众所周知的斐波那契晶格获得的。在本文中,我们发现了对该点集的修改,以使其散布明显低于斐波那契晶格的散布。我们的主要结果将暗示