In 3D the largest such set has size nearly linear in the radius X; in 4D it is linear; in all dimensions the size is at most order X to the d/2.
307, Birkhäuser/Springer, Cham
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Point sets avoiding near-integer distances
In 3D the largest such set has size nearly linear in the radius X; in 4D it is linear; in all dimensions the size is at most order X to the d/2.