Lower bounds for the Hausdorff dimension of n-dimensional self-affine sets

It was shown by Falconer [K. J. Falconer, The Hausdorff dimension of self-affine fractals, Math. Proc. Comb. Phil. Soc. 103, 339–350 (1988)] that there is an upper estimate for the Hausdorff dimension of a self-affine set embedded in n. This paper finds a corresponding lower bound for the Hausdorff dimension. We then show an example where the two bounds are very close.