When Does the Film "THX 1138" (1971) Take Place?

"THX 1138" is a science fiction film written by George Lucas with Walter Murch [adapting "Electronic Labyrinth: THX 1138 4EB" (1967) by George Lucas] that released March 11th, 1971. So when is "THX 1138" set? 

It takes place in the year: 

2187 AD 

We know this because early on the numbers "06/15/69", probably representing June 15th, 2169 AD, flash on the screen when THX 1138 asks for stronger drugs. So it must be during or after June of 2169 AD. 

Furthermore, when LUH 3417 is cited for a current "POSSIBLE DRUG VIOLATION" the screen reads "3/21/75" representing March 21st, 2175 AD. So it must be during or after March of 2175 AD. 

More specifically, when THX 1138 is looking for LUH-3417 the computer reports "LUH 3417  CURRENT POSITION:  REPRODUCTION  CENTR 34" and then reports new information about LUH 3417 for the audience with the numbers: "21/87" and "29/87". For this new information about LUH 3417 to be true, it must have changed since we last saw her and these numbers could represent current dates in 2187 AD. 

We know these dates ("69", "75", and then "87") are extremely unlikely to represent dates in the Twentieth Century or earlier because of the myriad technologies (video phones, bipedal robots, holograms, etc.) throughout the story that did not exist in the real world between 1901 AD and 2001 AD. Presumably, the first two dates are the birthdates of THX 1138 and LUH 3417 respectively. It could be during a century even later than the Twenty-First Century but the technology and environments hasn't progressed forward terribly much farther than the real-world Twentieth Century advancements and the work it's an adaptation of offers a specific option. 

The short film DOES have a clear time setting for the start of the narrative: 2187 AD. Assuming a close adaptation, this is the best year we can ascertain for the story. 

It was adapted to prose (novelization) in late 1971.