## What is the smallest time/space complexity class that is known to contain complxity class \$\mathsf{SPARSE}\$

Is it known if complexity class of all sparse languages is contained within e.g. $$\mathsf{EXP}$$ or $$\mathsf{EXPSPACE}$$? Or what is the smallest time or space complexity class that contains complexity class $$\mathsf{SPARSE}$$?