Oh my goodness, D.! She's probably the FIRST 16 year old girl to have sex in the history of time, too!
It's obvious by your reaction that she's sexually active WHY she's sneaking out to do it!
If you haven't already (and really why haven't you?), take her to the OB/GYN, get her some birth control, have her tested, buy her some condoms, right away.
You can use this as a bonding opportunity, she is a young WOMAN now, until we find a way to stop puberty from coming until their 21, they WILL be having sex as teenagers!
Have a (humble, non-threatening) talk with her. Tell her you want to make sure she's doing it for the right reasons, she doesn't feel pressure, she doesn't do it to hold onto her man, etc...
Let her know she can ALWAYS talk to you without fear of getting in trouble about EVERYTHING, especially SEX.
It's clear she doesn't feel safe NOW if she is sneaking out.
It's NOT ok to sneak out of the house at night, not SAFE, tell her you love her and are overwhelmed with the responsibility of keeping her SAFE.
It would break my heart if my daughter was afraid to come with me with the big issues in her life, she and I are a TEAM in business of her life. I'm sure there are some things she keeps from me, but overall we have a very open comfortable relationship.
I would be upset if I caught her sneaking out, but it's unlikely that'll happen. She doesn't NEED to sneak out.
Gotta show a non threatening interest in everything she does, draw her out, make her feel safe talking to you.
You think there's no sex at boarding schools?
She's 16 now, gonna have to change the way you motherhood somewhat.
I'm not sure it's anything her father needs to be involved in, unless he too will be loving and listen and guide her gently. Threats and punishments will only force her further away from both of you.
The goal is to keep her close.