MinT - Best Known (33, 33+26, s)-Nets in Base 16

Best Known (33, 33+26, s)-Nets in Base 16

(33, 33+26, 520)-Net over F₁₆ — Constructive and digital

Digital (33, 59, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (33, 60, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 30, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(33, 33+26, 642)-Net over F₁₆ — Digital

Digital (33, 59, 642)-net over F₁₆, using

3 times m-reduction [i] based on digital (33, 62, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 31, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(33, 33+26, 110189)-Net in Base 16 — Upper bound on s

There is no (33, 59, 110190)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 110434 874820 073611 653010 901514 262567 017507 822965 669626 440807 675111 758051 > 16⁵⁹ [i]