@Nca78 Not sure either to be honest, but technically I only did the calculation for a specific type of LED, the ones in the BOM.
I do use TSAL LEDs, and used http://ledcalc.com/#calc to do the resistor calculation for 7 LEDs with numbers extracted from the datasheet, leading to the ~5ohm resistor calculation.
I tried without any, or with a 4.7ohm resistor and I had significant better range results without resistor. Not a surprise, looking at the IR signal with a smartphone camera you can definitively see a brightness difference too, that's really a blaster
No burned LED after 48h of testing (sending one of my IR code every 5s). I also tried, for 10min, with regular red LED (http://www.nteinc.com/specs/3000to3099/pdf/nte3019.pdf) which have lower Vf and If requirements, no problems either.
I don't say that this is right, I truly don't have the background to do more than empirical experimentations, but it seemed good enough for me at the time. I did not had any problems since then, both with real TSAL from mouser and probably fake ones from aliexpress.