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The phrase "no such" is correct and usable in written English.
You can use this phrase to express the idea that something does not exist. For example, "The store was sold out of the shirt I wanted, but there was no such thing as a replacement."
Exact(60)
"No such kit".
"No such record exists".
But no such luck.
No such luck, alas.
There's no such place".
No such problem here.
No such problems here.
No such thing happened.
There's no such word.
But no such thing.
Alas, no such luck.
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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