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The phrase "based on either the" is correct and can be used in written English.
It is typically used to introduce a choice or alternative that is being considered. Here is an example: "The final decision will be based on either the cost analysis or the potential impact on the environment."
Exact(59)
Such methods are popular, but the collected compounds lack structural diversity, since they are all based on either the same or similar known scaffolds.
However, most research on this type of harvesters is based on either the simplified one-degree-of-freedom model or transfer matrix model.
Closing costs are based on either the cadastral value or the declared purchase price as it appears on the deed.
The program paid out grants to people based on either the pre-hurricane value of their homes or the estimated cost of rebuilding, whichever was less.
Circles would not disclose its fees, except to say that it has two pricing models, based on either the number of employees or the number of requests.
Two such distances are proposed, based on either the loglikelihood function, or the relative entropy.
Control designs based on either the Razumikhin or the Lyapunov-Krasovskii approaches are considered.
Various clinically relevant applications have been established for dual-energy CT based on either the differentiation or quantification of materials.
The timevarying FIR equalizers are derived based on either the matched filtering criterion, or the linear minimum mean-square error (MMSE) or the zero-forcing (ZF) criteria.
The selected countries employ different citizenship rules, based on either the principle of jus soli or jus sanguinis (or a hybrid form).
Similar(1)
PAD was defined based on either the results of peripheral Doppler analysis, or a history of amputation.
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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