Volume-discrepancy estimates in one and two dimensions

In one dimension, we give an estimate for the lower bound of the volume-discrepancy (see [1]) for any sequence and an estimate for the volume-discrepancy of the Van der Corput sequences in base b ≥ 2. In two dimensions, we estimate the volume-discrepancy for (0, 2)-sequences in base b ≥ 2 and give an explicit minimal net.