Before revision:  We show that  competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5. Furthermore, we show that for the input point sequences which are subsets of the infinite square or hexagonal lattices, / \log{\log{d}}), due to Charikar et al. (2004).
After revision:  We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least d+1 for every d \geq 1. This greatly improves upon the previous best lower bound, \Omega(\log{d / \log{\log{d}}), due to Charikar et al. (2004).