The difference between couldn't do, couldn't have done and can't have done

[Osakaki]

Hello dear English teachers, recently I have had difficulties using the modal verb "can" when trying to express that something didn't happen. Here is an example of what I find problematic:
He wasn't at the party. You ________ him there.
Which of the verb forms is appropriate here?
My guess is "You can't have seen him there" but I am really not sure. The only book about grammar I have got at home is intermediate grammar and it doesn't mention this.
Could you please give me a rule which would explain when to use couldn't, couldn't have done and can't have done?
Thank you, Lucie