Given an integer $n > 0$, let $f(n)$ denote the least dimension of the Euclidean space into which there exists a C^∞ isometric embedding of every Riemannian flat $n$-dimensional torus $\Bbb T^n =\Bbb R^n / L$, where $L$ is an $n$-dimensional lattice in $\Bbb R^n$.

What is known about $f(n)$ in terms of exact values, upper and lower bounds, or asymptotics?