Before revision:  This improves upon the previously best oracle complexity of O(n^2 (n + \log(R))) obtained by an elegant application of simultaneous diophantine approximation due to [Gr\"otschel, Lov\'asz and Schrijver, Prog.
After revision:  This improves upon the previously best oracle complexity of O(n^2 (n + \log(R))) for polynomial time algorithms obtained by [Gr\"otschel, Lov\'asz and Schrijver, Prog.