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All 126 strings from the video have been transcribed.
The printer randomly chooses a string of a pool of 41 strings in total (consisting of 32 long strings and 9 short strings).
There have been some other interesting discoveries, they can be found towards the bottom of the Google Docs page I linked in my comment above. People still don't have a clue as to what it could mean - any contribution or input is appreciated!
126 strings is indeed completely arbitrary.
I recorded 2 hours of printer footage (using a macro of course, my life isn't THAT sad).
And since one string takes about 1 minute (slightly less), I ended up getting 126 strings from those 2 hours of footage.
But the deal is: Because there isn't an infinite number of strings, strings starting repeating themselves. In fact, after only collecting 64/126 strings there aren't ANY original strings left! Every single string from 65 onwards has been seen in the first 64 strings.
(Take a quick look at the first list in the Google Docs document and you'll see what I mean.)
THEORETICALLY there could be a string left that we haven't discovered yet. In theory. But I figured that the odds of that are too slim to justify taking another look. If I ever find myself bored on a rainy sunday I'll definitely consider doing it though, for science.
Also: I found exactly 32 unique long strings (a "long string" consists of exactly 32 characters). So it's safe to assume that we found all of those, since 32 is such a nice, round number (power of 2).
As for the so-called "short" or "odd-length" strings (the ones that are shorter than 32 characters): We got nine of those. No idea why they're nine. They are really weird in general, come to think of it.
TL;DR: We don't know for sure whether we've gotten all the strings. But it's relatively safe to assume that we got all of them (I can guarantee you that we have all the long strings, not so sure about the short strings).
For a complete list of everything you need to know: Check out the bottom of the Google Docs document. (Use the structure tab on the left to navigate to "Interesting Discoveries")