Diaphony, discrepancy, spectral test and worst-case error

We also prove that the diaphony in base 2 coincides with the root mean square worst-case error for integration in certain weighted Sobolev spaces. This connection has also a geometrical interpretation, which leads to a geometrical interpretation of the diaphony in base 2. Furthermore we also establish a connection between the diaphony and the root mean square weighted L2 discrepancy of randomly digitally shifted points.