Yes, you can move out of your home at 16, but can't marry without parental consent until you're 18. But please do think carefully about doing so. Your parents will have good reasons for you not wanting to leave home when you still have a lot of emotional growing up to do. What we want at 16 is rarely what we want at 18 and without much experience of life, it's easy to think you'll be able to cope with the situations you might be confronted with.
Why do you want to move out of your home? Is it because of the discipline? Or because your parents don't like your boyfriend?