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In 1998, Burago–Kleiner and McMullen independently proved the existence of separated nets inR   d    which are not bi‐Lipschitz equivalent (BL) to a lattice. A finer equivalence relation than BL is bounded displacement (BD). Separated nets arise naturally as return times to a section for minimalR   d   ‐actions. We analyze the separated nets which arise via these constructions, focusing particularly on nets arising from linearR   d   ‐actions on tori. We show that generically these nets are BL to a lattice, and for some choices of dimensions and sections, they are generically BD to a lattice. We also show the existence of such nets which are not BD to a lattice.

Equivalence relations on separated nets arising from linear toral flows