<abstract xmlns="http://www.w3.org/1999/xhtml">We give a complete classification of all matrices <italic>C</italic>1,<italic>C</italic>2,<italic>C</italic>3 ∈ <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_udt-2019-0004_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>C</mi></mrow><mn>3</mn></msub><mo>∈</mo><msubsup><mrow><mi>𝔽</mi></mrow><mn>2</mn><mrow><mi>m</mi><mo>×</mo><mi>m</mi></mrow></msubsup></mrow></math><tex-math>{C_3} \in \mathbb{F}_2^{m \times m}</tex-math></alternatives></inline-formula> which generate a digital (0,<italic>m,</italic> 3)-net in base 2 and a complete classification of all matrices <italic>C</italic>1,<italic>C</italic>2 ∈ <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_udt-2019-0004_eq_002.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>C</mi></mrow><mn>2</mn></msub><mo>∈</mo><msubsup><mrow><mi>𝔽</mi></mrow><mn>2</mn><mrow><mi>ℕ</mi><mo>×</mo><mi>ℕ</mi></mrow></msubsup></mrow></math><tex-math>{C_2} \in \mathbb{F}_2^{\mathbb{N} \times \mathbb{N}}</tex-math></alternatives></inline-formula> which generate a digital (0, 2)-sequence in base 2.</abstract>

We give a complete classification of all matrices C1,C2,C3 ∈ C3∈𝔽2m×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∈𝔽2ℕ×ℕ{C_2} \in \mathbb{F}_2^{\mathbb{N} \times \mathbb{N}} which generate a digital (0, 2)-sequence in base 2.

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

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

We give a complete classification of all matrices C1,C2,C3 ∈ C3∈𝔽2m×m{C_3} \in \mathbb{F}_2^{m \times m} which generate a digital (0,m, 3)-net in base 2 and a...

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

Publié en ligne: 27 mars 2020

Pages: 43 - 52

Reçu: 11 juin 2018

Accepté: 22 août 2018

DOI: https://doi.org/10.2478/udt-2019-0004

Mots clés
digital nets, digital sequences, classification of generating matrices

© 2019 Roswitha Hofer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Publié en ligne: 27 mars 2020

Pages: 43 - 52

Reçu: 11 juin 2018

Accepté: 22 août 2018

DOI: https://doi.org/10.2478/udt-2019-0004

Mots clésdigital nets, digital sequences, classification of generating matrices

© 2019 Roswitha Hofer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
digital nets, digital sequences, classification of generating matrices