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"maximum number allowed" is a correct and usable phrase in written English.
You can use it to refer to the greatest number of something that is permitted or reasonable. For example, "The maximum number allowed for this tour group is twenty people."
Exact(18)
Split the items so you each stay within the maximum number allowed and then get out the door quicker.
— Fourteen horses, the maximum number allowed, entered the starting gate for the Blue Grass Stakes at Keeneland Race Course.
Now, with the race just two days away, he needed to identify sixteen, the maximum number allowed, to take with him to Anchorage.
And respondents greatly underestimated true staff levels with a median estimate of about 10 —nearly half the maximum number allowed to House members.
LimeBike, and its competitors Spin and Mobike, say they each have deployed 400 bicycles, the maximum number allowed under city permits.
It would have amounted to an $80,000 annual payment to the city from each company that deploys 400 vehicles — the maximum number allowed under the city's rules.
Similar(42)
n represents the maximum copy number allowed for any gene and m represents the maximum number of GD events to be considered.
The values are still in the inadmissible range, since the maximum acid number allowed in the ASTM D6751 is 500 mg kg−1.
Rogers said MIT is funding 240 empty beds this year, but the maximum number of allowed empty beds will decline each year, as will the funding.
The iteration will terminate when a maximum number of allowed iterations have passed without improvement.
The stop condition is usually the maximum number of allowed iterations for PSO to execute or the minimum error requirement.
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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