Can’t get rid of “other” in iPad storage

Some of that "Other" data could be related to cached files for some of the apps you have on your device. Some of that data may also be related to iOS Analytics. Do you have analytics enabled in Settings > Privacy > Analytics? You can see all the logs under Analytics Data.

Your best bet at this point would be to manually back up any media you need and set the iPad up as new without restoring from a backup. You'll still get back your iCloud data, but you won't be loading on any cache or analytics files back on to the device. You would lose your message history on the iPad and would need to redownload your apps from the App Store, but it's an option.

If you have a computer: Restore your iPhone, iPad, or iPod to factory settings -

If you don't have a computer or prefer to reset from iOS: How to erase your iPhone, iPad, or iPod touch - 

Did you restore from your iCloud backup? If so, it's possible you loaded the cached files back on to your device. How much more space are you trying to clear and what's taking up the most space under Settings > iPad Storage aside from Other?

This article from  support describes a bit about what "Other" is in iOS storage: How to check the storage on your iPhone, iPad, and iPod touch)

Specifically, look at the section titled: About cached files in "Other" iOS storage.

Also, are you using iCloud Photo Library? Doing so can help clear up space on your device by creating optimized versions of your photos and videos.

Keep in mind that a 16GB device fills up fairly quickly depending on how many apps, movies, music, photos, and videos you have downloaded, as well as Messages attachments. I recommend deleting (or transferring to another device) any media or message attachments you don't need or use regularly.

A portion of that data may also be related to the system. When you're in the Storage Settings and you swipe all the way to the bottom, how much space is the "System" taking up?

I’m glad I could help!