We know for sure that a fully working iOS 10.1.1 jailbreak is not going to be available for some time. A picture was posted on the internet by Luca Todesco, who is a known iOS hacker, and in this picture he shows an iPhone 7 that has its iOS 10.1 jailbroken. This picture shows us that the new OS is not impenetrable, and a new jailbreak might be released.
The Chinese hacker group called Pangu was the last ones to release a fully functional jailbreak for iOS. The jailbreak tool that Pangu offers is for the 9.3.3 iOS version. iOS 10 still remains untouched, and a fully functional jailbreak for it has yet to be released.
The recently released 10.1.1 iOS came with a few fixes to repair some known problems that the Health app had. The iOS hacker Luca Todesco proved to us that it can be jailbroken, but he is not going to release the jailbreak tool any time soon.
A video has recently surfaced on Reddit that showcased a fully functional iOS 10.1 jailbreak. Most of the comments were pointing out that the video is fake, even Saurik commented saying that he believes the video is fake. Saurik is the creator of Cydia.
The only reliable hacking group that we can expect to release the new jailbreak tool is Pangu. There are rumors saying that Pangu is currently working on developing a new jailbreak tool to bypass the security iOS 10.1.1 has. They have already posted a video to demonstrate that they are getting close to achieving their goal.
Even if Luca Todesco has discovered a way to jailbreak the new iOS, he is not going to released it to the public, and this is not the first time he did this. He also teased the public with other jailbreak tools for older version of iOS but did not release them. All we can do is wait for Pangu, or other developer group to release a complete jailbreak iOS tool.