My iPhone 16 Pro Max is not showing iOS 26

At this time, the software is only available to registered developers.

The public beta will be available sometime in July. Info here:

Apple Beta

Pay very close attention to Apple's strong recommendation to only install the beta on a spare phone.

Not surprising since it won't be released to the public for several months...

iOS 26 is only available for developers. Are you a registered developer?

If you do not have a spare phone – or do not wish to be a "guinea pig" for testing incomplete software that may be full of major bugs – you should avoid beta versions.