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Delone set

The red points form part of an ε-net for the Euclidean plane, where ε is the radius of the large yellow disks. The blue disks of half the radius are disjoint, and the yellow disks together cover the whole plane, satisfying the two definitional requirements on an ε-net.

In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are. These sets have applications in coding theory, approximation algorithms, and the theory of quasicrystals.

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