On the exact tt-value of Niederreiter and Sobol’ sequences

This paper studies several well-known families of (t,s)(t,s)-sequences. First we determine the exact tt-value of Niederreiter sequences. Then we analyze the exact tt-value of generalized Niederreiter sequences and we show that, for a range of dimensions of practical interest, Niederreiter–Xing sequences are demonstrably better than Sobol’ sequences in terms of the exact tt-value. Previously, such a conclusion was not possible since only upper bounds on the exact tt-value of these sequences and a general lower bound for all (t,s)(t,s)-sequences were available.