It sounds like you might need some help in the classroom, 16 to 1 is asking a lot from you. Do you have a boss or someone who can help? If you could remove some of the most out of control kids from the room during nap time, you might be able to get the rest under control. Do you have someone who could look after some kids during these periods?

Assuming that extra help is not an option... sounds like you need to pick and choose your battles. Try picking one thing that they are doing wrong to focus on, and discuss it with the child and the parents. I wouldn't suggest bribes as they may come to expect it, and only behave for rewards. Denying toys or privileges should only be done when you know you can follow through with it. Kids are experts at getting what they want.

Another suggestion, after talking to a preschool/early childhood expert:

Try making up a 'special job' for a few of the problem children. Just tell the child individually that you have a special job for them, something that they can help you with (eg: bringing you all the paintbrushes so you can clean them). Thank them when they do it, and tell them it was very helpful, and why it was helpful. This helps create a bond between you and the child, gives them a positive reinforcement unrelated to his/her usual bad behavior actions, and breaks the bad behavior cycle. Hopefully with this improved bond the child will care more about what you say and your authority. It also helps them to focus on one thing, and hopefully do it. You should try to coordinate this with nap time, or other times when they are being disruptive to allow the other children to settle down, or focus on what they should be doing.

Hope this helps! Classroom management is tough.