Dyadic diaphony of digital sequences par

The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital (0, s)-sequences over Z2, s = 1, 2. These formulae show that for fixed s ∈ {1, 2}, the dyadic diaphony has the same values for any digital (0, s)-sequence. For s = 1, it follows that the dyadic diaphony and the diaphony of special digital (0, 1)-sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital (0, s)-sequences and show that for s = 1 it satisfies a central limit theorem.