A new look at discrete discrepancy

The objective of this paper is to study the issue of discrete discrepancy [Hickernell, F.J., Liu, M.Q., 2002. Uniform designs limit aliasing. Biometrika 89, 893-904; Fang, K.T., Lin, D.K.J., Liu, M.Q., 2003. Optimal mixed-level supersaturated design. Metrika 58, 279-291; Qin, H., Fang, K.T., 2004. Discrete discrepancy in factorial designs. Metrika 60, 59-72], which has wide application to the field of fractional factorial designs. Here we present an improved lower bound to discrete discrepancy.