Thank you for all your answers, it helped me see better.
I first re-did my schematif with a 1117, but in the end found those parts :
-Microchip TC1054/TC1055/TC1186
-Microchip TC1014/TC1015/TC1185
-Micrel (now Microchip) MIC5205
-TI TLV700
They all are 3.6V LDO, available with 100mA or more max Iout, have adropoout of less than 0.3V (and 0.1 in my case where I need low current).
The only difference is pin 4 :
-MIC5205 and TC1014/TC1015/TC1185 have an optionnal cap to GND for ultra-low-noise
-TLV700 has it unconnected
-TC1054/TC1055/TC1186 uses it as an output for error detection
I'll save the two resistors and the cap (I'll put pads so I can add one if needed)
Thank you,
John.