ABSTRACT
If one orders the primitive polynomials over F2 by degree p1(x), p2(x), . . ., then the Sobol’ sequence yields a (ts, s)-sequence in base b = 2 for each s where ts =∑s−1
i=1 (deg pi − 1). Unrelated to this, the Niederreiter sequence in any prime power base q yields a (Tq(s), s)-sequence where Tq(s) =
∑s i=1(deg pi−1) for any collection of
pairwise relatively prime polynomials p1(x), p2(x), . . . of positive degree over Fq [1678, Sec. 4.5] so that, in particular, T2(s) < ts for s ≥ 8 if polynomials of lowest possible degree are chosen for the construction of the Niederreiter sequence.
