I know that P = PSPACE is a famous open problem, and that EXPTIME = NEXPTIME is also unknown. By the time heirarchy theorem we know that NP is a strict subset of NEXPTIME.
Is anything known about the relationship between PSPACE and NEXPTIME? What about under the assumption that P = NP or that P != NP? Are the containments open problems from PSPACE all the way to NEXPTIME?