CATIIIa
No it remains general that way: CAT IIIa DH, usualy 50ft or higher. Remind you that the HUD Airplanes = B737, B787, EMB´s can do manual CAT IIIa Approaches with 50ft DH.
The chain must be strong enough to hold the weakest part. CAT IIIb has as well some DH´s at the discretion of the regulatory Authorithy. You have a AH and they require you also a DH in some cases. I do not agree with the 25ft that some Desk flyer decide, the moment the AT walks to idle and the G/A takes even longer to accelerate if you opt for the G/A. We discussed that issue with the DGCA but the opposite result was offered: DH 50 ft for CAT IIIb, a clear sign of not understanding what the system is capable for and how it is designed. It was just to show muscle.... but no brain.
Fly safe and land happy
NG