No, not only should you not use a traditional box spring with a Nest Bedding mattress, but doing so may void its warranty. Instead, they suggest using a flat surface, like a platform foundation, or a base with slats no greater than 4 inches apart.
Nest Bedding considers traditional box springs to be an improper support system due to their flexible coils.
During a warranty claim, they will ask for a photo showing the foundation used on the mattress, and a box spring will be a cause to deny the claim.
