Denote by . For each let the number of occurences of the tuple t in the sample. This statistic is asymptotically distributed with degrees of freedom. In Stefan Wegenkittl's master thesis you can find 3-D bar plots which summarize the behaviour of linear and inversive congruential generators for sample sizes and dimensions . Each bar reports the minimum between 2 and the value of the KS test statistic .
Black bars indicate rejection.
The grey level of the other bars varies between white if the KS-test statistic is zero and deep grey near the critical value. The 32 values are arranged in a rectangle containing 4 rows and 8 columns. A black subrectangle denotes a high lower-tail probability indicating that some differences are untypically large. White subrectangles on the other hand denote almost equally filled up counters, i.e., untypically small values of the overlapping serial test statistic. The plots are organized in such a way that again a single figure contains results in all analyzed dimensions and sample sizes.