Adelic constructions of low discrepancy sequences (Q2885121)

With the use of Mahler's variant of Minkowski's theorem on a convex body in a field of series and considering lattices in \(s+1\) dimensional space \((\mathbb F_q((x^{-1})))^{s+1}\) the author constructs uniformly distributed sequences in \([0,1]^s.\) To be more precise, to construct a so called \((t,s)\) sequence for some \(t\) the author uses admissible lattices proposed by Armitage, who obtained such lattices by constructing a special algebraic extension of \(\mathbb F_q(x).\) To construct such sequences for all \(t\) another result of Armitage, concerning the construction of the lattice from an arbitrary extension of \(\mathbb F_q(x)\), is used. It should be mentioned that Halton's construction of low discrepancy sequences is also used.