We show that, for every set of n points in  d-dimensional unit cube, there is an empty axis-parallel box of volume at least \Omega(d/n) \to . In the opposite direction, we give a construction without an empty axis-parallel box of volume O(d^2\log d/n). These improve on the previous best bounds of \Omega(\log d/n) and O(2^{7d}/n) respectively.
We show that, for every set of n points in the d-dimensional unit cube, there is an empty axis-parallel box of volume at least \Omega(d/n) as n\to\infty and d is fixed . In the opposite direction, we give a construction without an empty axis-parallel box of volume O(d^2\log d/n). These improve on the previous best bounds of \Omega(\log d/n) and O(2^{7d}/n) respectively.
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the
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as n
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\infty and d is fixed