Apple stopped singing iOS8.1.1 yesterday. That means you can’t downgrade or upgrade your device into iOS 8.1.1 anymore. Apple will force you to get iOS8.1.2. In other hand there is no requirement of go for iOS 8.1.1 because iOS 8.1.2 is much better and it’s jailbreakable. You can jailbreak iOS 8.1.2 using Taig 1.2 and complete jailbreak tutorial with Taig Download links are available here.
It’s highly recommended to upgrade your device to the iOS 8.1.2 and jailbreak as soon as possible since Apple already released iOS 8.2 beta versions for developers. Apple will stop signing iOS 8.1.2 also when they release iOS 8.2. iOS8.2 jailbreak will not possible for a while although TaiG team said they can jailbreak iOS 8.2 with the same tool. We advice you to have the best possible solution at the moment other than waiting for unknown perfect solutions.