The $b$-adic diaphony of digital sequences

The $b$-adic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this article we give a formula for the $b$-adic diaphony of digital $(0, s)$-sequences over $\mathbb{Z}_b$, $s=1, \ldots, b$. This formula shows that for a fixed $s \in {1, \ldots, b}$,the $b$-adic diaphony has the same values for any digital $(0, s)$-sequence over $\mathbb{Z}_b$. For $t > 0$ we show upper bounds on the $b$-adic diaphony of digital $(t, s)$-sequences over $\mathbb{Z}_b$. We also consider the asymptotic behavior of the $b$-adic diaphony of these digital sequences.