iOS 7.1.1 was launched 2 weeks ago and a lot of people are actually waiting for an iOS 7.1.1 jailbreak. It is true that you can jailbreak an iPhone 4 running iOS 7.1.1, but that jailbreak is tethered and unfortunately only available for that specific phone model.
iOS 8 beta 1 should be available in less than 1 month and you can imagine that no one will release a jailbreak now for iOS 7, just because they might use an exploit that is opened on iOS 8 too.
So basically, if you are waiting for a jailbreak sollution for iOS 7.1.1 – it won`t come up anytime soon.
Don`t get fooled and don`t try to jailbreak your iOS 7.1.1 with software that promises to. You will find the news on BCT if something is legit.