MinT - Best Known (71−33, 71, s)-Nets in Base 16

Best Known (71−33, 71, s)-Nets in Base 16

(71−33, 71, 518)-Net over F₁₆ — Constructive and digital

Digital (38, 71, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (38, 72, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(71−33, 71, 642)-Net over F₁₆ — Digital

Digital (38, 71, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (38, 72, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 36, 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]

(71−33, 71, 84028)-Net in Base 16 — Upper bound on s

There is no (38, 71, 84029)-net in base 16, because

1 times m-reduction [i] would yield (38, 70, 84029)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 942746 042083 527021 385554 772513 779172 678690 946049 525597 456437 180202 012839 606027 974461 > 16⁷⁰ [i]