Discrepancy bounds for infinite-dimensional order two digital sequences over F₂

Original · EN

In this paper we provide explicit constructions of digital sequences over the finite field of order 2 in the infinite dimensional unit cube whose first N points projected onto the first s coordinates have Lq discrepancy bounded by r³/²⁻¹/q √m₁ˢ⁻¹ + m₂ˢ⁻¹ + + mᵣˢ⁻¹ N⁻¹ for all N = 2ᵐ¹ + 2ᵐ² + + 2ᵐʳ ≥ 2 and 2 ≤ q < ∞. In particular we have for N = 2ᵐ that the Lq discrepancy is of order m⁽ˢ⁻¹⁾/² 2⁻ᵐ for all 2 ≤ q < ∞.