Not

negation

forme

• not or n't

predeterminer

Some deny the existence of determiners (articles, demonstratives, quantifiers), so the idea that a grammatical class such as predeterminers should exist is not always welcomed easily, especially by those who teach what is known in France as la grammaire scolaire.

• Not a one
• Not everybody
• not some time later (6m examples at Google, not a few of which are difficult to evaluate grammatically)
• not a few of which
• not the least of which

In any case, it is clear that the boundaries between adverbs and determination in the noun phrase (particularly deictic determination: today, tomorrow, this, that) are relatively fuzzy. At least four of the examples would clearly seem to be noun phrases.