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The phrase "a random number list" is correct and usable in written English.
It can be used when referring to a collection of numbers that are generated without any specific pattern or order.
Example: "For the experiment, we need to generate a random number list to ensure unbiased results."
Alternatives: "a list of random numbers" or "a list of numbers generated randomly".
Exact(17)
Novice residents and final year medical students were randomized into two equal groups using a random number list.
All legs were given a number from a random number list.
Households along this imaginary line were then counted and a household randomly selected using a random number list.
The order of the mackerel and squid allocation was randomly determined using a random number list, with the identification number on the top of each dish.
We used a random number list to select patients randomly from the practice diabetes register until a total of 21 patients were recruited in each practice.
Then an independent person randomized the patient to either the intervention group or the control group, using a random number list and sealed envelopes.
Similar(43)
Respondents were randomized using a random numbers list without stratification into one of two conditions: (i) an Internet personalized alcohol feedback condition (intervention condition); or (ii) a no-intervention control condition.
The randomization was based on a random numbers list.
Randomization was conducted using a random numbers list (odd numbers for condition one and even numbers for condition two) with no stratification.
An independent statistician (FK) generated a random numbers list which, by permutation of random blocks, block size 9, was balanced for treatments within strata.
We numbered the households consecutively, and generated a random-number list using the SPSS random function.
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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