iOS 11.1 Jailbreak
Earlier this year jailbreak developers teased an iOS 11 jailbreak. Since then we haven't heard, or seen, much.
We typically see a proof of concept ahead of a jailbreak release and jailbreak developers haven't publicly teased anything related to the iOS 11.1 beta or iOS 11.1 update. This doesn't rule anything out, but it doesn't instill confidence.
Popular jailbreak developer, and creator of the Yalu jailbreak, Luca Todesco stated he would "stop all public iOS research" after the release of the iOS 10.2 jailbreak. That doesn't instill much confidence either.
An iOS 11.1 jailbreak isn't out of the question, but we aren't getting our hopes up. For now, you must be on iOS 10 or iOS 9 to jailbreak an iPhone or iPad and there's no way to downgrade to either one.