Asymptotically optimal t-design curves on the Grassmann manifold

Similarly to well-known spherical t-design points, we investigate t-design curves on the Grassmannian manifold Gr2,4. Such curves have the special property that the line integral along them integrates polynomials of degree t exactly. We derive asymptotic bounds on the length of such curves based on a parametrization of Gr2,4 as $\left( {{\mathbb{S}^2} \times {\mathbb{S}^2}} \right)/ \pm 1$.