Earth 38: Supergirl
Might be a nod to the debut of Superman (1938) as mentioned in another answer.
Earth 16: Future Oliver
The debut episode of future Oliver was in Legends of Tomorrow during first season (2016)
Earth-99: Future evil Batman
Might be a nod to DCAU (Batman Beyond premiered in 1999)
Earth-75 Dead Superman
Issue #75 when Doomsday killed Superman.
The number 167 is a nod to the show's producers Alfred Gough and Miles Millar both being born in 1967. source
Earth-96 Brandon Routh Superman
Must be a reference to Kingdom Come (1996)
Earth 203 Bird of Prey
Birds of Prey (TV series) ended on 2003
Based on comics and numbered similarly
Earth-18 Active Lazarus pit
In comics, it was wild west earth. We only see Jonah Hex (Not part of comics earth 18) who is a western hero.
Earth 9: DC Universe's Titans
Black Lightning and Nash Wells/Pariah earth is not numbered