MinT - Best Known (28, 50, s)-Nets in Base 16

Best Known (28, 50, s)-Nets in Base 16

(28, 50, 520)-Net over F₁₆ — Constructive and digital

Digital (28, 50, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 25, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(28, 50, 642)-Net over F₁₆ — Digital

Digital (28, 50, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (28, 52, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 26, 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]

(28, 50, 97312)-Net in Base 16 — Upper bound on s

There is no (28, 50, 97313)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 606974 744820 590813 625049 717301 426888 022662 462949 725009 860896 > 16⁵⁰ [i]