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The phrase "a substantially higher number" is correct and usable in written English.
It can be used when comparing quantities or statistics to indicate that one number is significantly greater than another.
Example: "The survey results showed a substantially higher number of participants favoring the new policy compared to the previous year."
Alternatives: "a significantly larger amount" or "a markedly greater figure".
Exact(20)
In particular, the propene flames produce a substantially higher number of soot nuclei than in the ethylene flames.
EDC-modified native TRP47, recombinant GST-TRP47 and GST-CterTRP47 having a substantially higher number of acidic residues compared to the basic residues (ratio of 2∶1 to 6∶1) migrated much faster than the unmodified protein, close to their predicted molecular masses as observed by others [52].
In a larger tumor, and in tumors with higher mutation rates due to genetic instability, or tumors with certain death rates, a substantially higher number of new MHC I epitopes is generated, such that a clinically detectable tumor may harbor hundreds of tumor-specific epitopes.
Interestingly, we noted that a substantially higher number of patients had elevated TWIST1 mRNA levels in our present study [ 4].
We detected a substantially higher number of significant gene expression patterns in comparison to commonly used enrichment tests.
The high dose group in the VA/NIH study [ 7] suffered a substantially higher number of complications, such as haemodynamic instability and electrolyte disturbances.
Similar(40)
Application of this model to an example situation showed that, even under optimistic measurement conditions, a substantially high number of test replicates would be required.
Although the country-level admission rate was highest in Djibouti at 14.6%, the refugee population in Sudan, with a 12.4% enrollment rate, is seven times larger and contributed substantially higher number of enrollment.
An appropriately defined kernel function allows the computations to be performed in the original input space and facilitates extraction of substantially higher number of principal components enabling excellent denoising and feature extraction capabilities.
While the other place profile was absent in Poland, big home profile had substantially higher number of contacts, maybe indicating that contacts located in other place in other countries occur at home in Poland.
This difference was mainly explained by the substantially higher number of intrauterine fetal deaths in deprived neighbourhood pregnancies (20/2,779 versus 17/4,580).
More suggestions(18)
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a substantially higher tumorigenicity
a substantially higher cost
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a substantially higher activity
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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