First, don't punish him! I highly doubt he is intentionally deciding not to use the restrooms because he just feels like being naughty, these are accidents that he is unable to avoid. I'm sure the embarrassment of them is more then enough punishment to make him want to stop them, further punishment will not help. Worse, punishing him for accidents he can't control sends a bad message, causing him to feel guilty or bad about things outside of his control. It may also cause punishments for other behaviors to be less effective, if he starts thinking of punishments being because of things outside of his control and thus not something he can avoid.
If the accidents are actually only happening at daycare then I would try to determine what is different about his daycare. Have you talked to him about this? Does he have trouble going to the bathroom, is he afraid to go etc? Does he know he needs to go to the bathroom, or not realize until after his accident occurs?
The most common cause I've seen for accidents like this during the day time has been distraction. The child is so busy that he does not realize his own needs until the accident occurs, a problem I have seen at much older ages. However, the reason I see that so often is because I worked a bit with special needs children and kids with ADHD, and ADD/ADHD children are far more prone to hyperfocus which can cause them to miss their other needs. I'm not sure how this is to be a problem with non ADD children.
Though, again, if it's really only at his daycare it may be an issue with the daycare. Shyness and being afraid to ask to use the restroom has already been mentioned, likewise a shyness or fear to use the restroom at the daycare could theoretically be an issue as well. The important thing is to talk with your son and figure out what he is feeling and what he is thinking when he feels the need to use the restroom.
Finally, the easiest short term solution is to set up a schedule, as already mentioned. Pick a few times during the day and have him always use the restroom then, before nap time, after snacks etc. Work with his teacher to have her remind him of these restroom times, and encourage him to try even if he doesn't need to. Eventually he will learn to simply use the restroom at these times during the day without further prompting from the teacher. The key thing is to pick times that are easy for him to remember and learn, so he can eventually learn when he should go without prompting from the day care, as it sounds as if they are either frustrated with prompting him or occasionally forgetting leading to accidents.