Apple now offers 3C39 firmware for the AirPods Max. The previous headset update was version 3C16. This goes back to last December.
AirPods Max update with 3C39 firmware
Apple’s headphones debuted with 3B71 firmware. There was then an update numbered 3C16. And here is today the 3C39 firmware for the AirPods Max. Unfortunately, there is no information available on new features or bug fixes. Apple never communicates details about this. It’s the same with AirPods and AirPods Pro.
The installation of the new firmware for AirPods Max is done automatically, in the background. There is no real way to force the switch to the new version. It’s a shame, but unfortunately that’s how it is. You have to wait for the headset to decide on its own to search for an update to download and install it.
To check the firmware, go to Settings> General> Information, go down and select your AirPods Max. The firmware version is located in the “Version” line.