A Complete Classification of Digital (0,m, 3)-Nets and Digital (0, 2)-Sequences in Base 2

Abstract

Abstract We give a complete classification of all matrices C1,C2,C3 ∈ C3∈𝔽 2m×m {C_3} \in \mathbb{F}_2^{m \times m} which generate a digital (0,m, 3)-net in base 2 and a complete classification of all matrices C1,C2 ∈ C2∈𝔽 2ℕ×ℕ {C_2} \in \mathbb{F}_2^{\mathbb{N} \times \mathbb{N}} which generate a digital (0, 2)-sequence in base 2.