  We deal with lattices that are generated by the Vandermonde matrices
associated to the roots of Chebyshev-polynomials. If the dimension $d$ of the
lattice is a power of two, i.e. $d=2^m, m \in \mathbb{N}$, the resulting
lattice is an admissible lattice in the sense of Skriganov. Those are related
to the Frolov cubature formulas, which recently drew attention due to their
optimal convergence rates in a broad range of function spaces with mixed
smoothness. We prove that the resulting lattices are orthogonal and possess a
lattice representation matrix with entries not larger than $2$ (in modulus).
This allows for an efficient enumeration of the Frolov cubature nodes in the
$d$-cube $[-1/2,1/2]^d$ up to dimension $d=16$.
