>>132822813notable character as in it's a character that the plot revolves around and is given perspective from, I'd imagine.
And besides, for a character to be an anti-hero in the first place they should be a character with a role in the story that typically has heroic qualities.
For example you don't look at a side character (that can be good or bad because this character is just an existence to drive the plot forward) that has little to no impact to the story and does no drive the perspective of how the audience views the plot whatsoever and say "this character is supposed to be a good guy, but he's actually doing something bad under the assumption that he's doing good, he must be an anti-hero!"