Construction of subspaces with known Diophantine exponents for the last angle

Schmidt generalized in 1967 the theory of classical Diophantine approximation to subspaces of ${\mathbb{R}}^n$. We consider Diophantine exponents for linear subspaces of ${\mathbb{R}}^n$ which generalize the irrationality measure for real numbers. Using geometry of numbers, we construct subspaces of ${\mathbb{R}}^n$ for which we are able to compute the associated exponents for the last angle.