In the design of experiments, the Design Resolution is a key criteria for selecting a fractional factorial design:
||two factor interactions are aliased with main effects
||two factor interactions are aliased with other two factor interactions, but not with main effects. Main effects are aliased with three factor interactions.
||two factor interactions are not aliased with each other, but are aliased with three factor interaction
An RIII design would usually be used for screening experiments. There would rarely be any point in going beyond an RV design.
In general the resolution is the length of the shortest word in the defining relationship.