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The phrase "a relatively restricted set" is correct and usable in written English.
It can be used when describing a group or collection that is limited in scope or variety compared to a larger context.
Example: "The study focused on a relatively restricted set of variables to ensure a more controlled analysis."
Alternatives: "a somewhat limited group" or "a fairly narrow range".
Exact(2)
We identified a relatively restricted set of 117 regulated genes, the majority (90) being upregulated by light.
This might be interpreted such that the dendrites of these neurons pick up information from a relatively restricted set of afferent fibers that make a maximal traverse through the dendritic arbors of individual neurons.
Similar(58)
Apple has reserved the NFC chip for a fairly restricted set of capabilities.
These shared sequences begin and end with a notably restricted set of glyphs.
Madagascar is the world's fourth-largest island, but it is still a relatively restricted space.
"So we've got a double whammy – there is terrific demand coupled with what looks like a relatively restricted supply over the next four or five months".
Compared to past works, the "London Pictures" have a relatively restricted palette: tabloid black and white, highlighted with blood red.
On the negative side, Michelson interferometers have a relatively restricted wavelength range and require use of prefilters which restrict transmittance.
Besides, in the Netherlands, there is a relatively restricted antibiotic policy.
Shared genes had a relatively restricted tissue co-expression with interactors, contrary to specific genes.
Integrins have a relatively restricted, cell type-specific and context-dependent expression with defined substrate specificity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com