Why can't I download iOS 16.1.1?

You need to correctly Identify your iPhone model - Apple Support

These are the iOS options based on iPhone Model -->

• iOS 16.1.1 --> SE (2nd and 3rd Gen), 8 / 8 Plus, X, XR, XS /XS Max, 11,11 Pro /11 Pro Max, iPhone 12, 12 Mini, 12 Pro, 12 Pro max, iPhone 13, 13 Mini, 13 Pro, 13 Pro Max, 14, 14 Plus, 14 Pro and 14 Pro Max
• iOS 15.7.1 —> 6S / 6S Plus, SE (1st Gen), 7 / 7 Plus,
• iOS 12.5.6 —> Final release supported on iPhone 5S, iPhone 6/6 Plus, 
• iOS 10.3.4 --> iPhone 5
• iOS 10.3.3 --> iPhone 5C
• iOS 9.3.6 --> iPhone 4S
• iOS 7.1.2 --> iPhone 4

Learn how to...

• Over-the-Air Update --> Update your iPhone or iPad - Apple Support (IN)
• Update using iTunes/Finder --> Update your iPhone, iPad, or iPod touch with iTunes - Apple Support (IN)

This problem is often brought about by the breakdown of the Apple server or a system error on your iPhone. Also, some other reasons will also cause the iOS update not to show up. Take a look at some common ones: Apple server went down because millions of people update the iOS system at the same time.