We know that most Star Wars droids were designated using 4 letters of High Galactic alphabet (which is basically Latin so base 36 including numbers).
Then, the upper bounds on named R2 units would seem to be be 36^2=1296 even assuming random 2 letters at the end, and 26*10=260 assuming the typical naming scheme of Letter+Digit.
Is there any notion in canon of just how many R2- units were ever produced?
Wikia (unsourced) says:
he R2-series astromech droid was a model of astromech droid produced by Industrial Automaton, boasting a level of success that was never equaled in Industrial Automaton's long history. A combination of excellent design, high-quality marketing, and good timing made this astromech droid one of the most sought after droids in history, and one of the few vintage astromech series still in active production decades after it was first designed, including the prototype R2-0. The line was so successful that the Galactic Empire took credit for the design.
Given the size of the Galaxy (millions? of inhabited planets, gazillions of beings), a production run of 260 - or even 1296 - seems to square very poorly with "one of the most popular astromeh droids in history with multi-decade production run".
Is there ever a canon explanation (ANY canon) for this?
- Were there tons of non-designated R2 units?
- Were later models designated differently, perhaps not limited to R2-$L$D scheme?
- Were there really only 260 or 1296 R2 units in the entire galaxy? Some other explanation?
- Was the assumption that such designation was a unique proper name - implied by the use of ArtooDeetoo as a proper name in the movie as well as similar references to all other droids - wrong and such designations were in fact reused for multiple droid units?