Sure, the Oberth can be an old Vulcan design from 2178 or so. But there's no actual evidence for such an intent - there's just material we can pretend to be evidence for such an outcome.
Actual intent is currently unknown and a subject of individual interpretation and preference.
If we go by the registry and assume FJ's System is applicable. i.e. the higher the number the stronger the ship, then it's "17" for the Enterprise
and her sister ships, "18" for the Miranda Class and "20" for the Excelsior Class (conclusion: Reliant
is stronger than Enterprise)
if we go by the registry and assume Matt Jefferies' System is still applicable than the first two digits indicate a chronology in ship building / design series.
"17" in TOS and the first film, "18" (one in the starship status chart and) in the second movie, "20" in the third movie for the latest starship design (Excelsior Class).