A good permutation for one-dimensional diaphony

In this article we focus on two aspects of one-dimensional diaphony F(S ^σ _b, N) of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574... for a permutation in base 19 to 1.13794... for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version X̃, we analyse the connection between the diaphony F(X, N) and the L ₂-discrepancy L ₂(X̃, N) using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.