Is the ATMEGA328P's serial baud rate quantised?
It is a fully digital system. It must operate in discrete steps.

This is the formula from the datasheet:


UBRR register is 16 bits wide (UBRRL + UBRRH), so it can only lead to 65536 possible baud settings.

Look also at section "24.11. Examples of Baud Rate Setting" and table 24-4 of the datasheet.