Construction of subspaces with known Diophantine exponents for the last angle

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