MinT - Best Known (85−40, 85, s)-Nets in Base 16

Best Known (85−40, 85, s)-Nets in Base 16

(85−40, 85, 518)-Net over F₁₆ — Constructive and digital

Digital (45, 85, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (45, 86, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 43, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(85−40, 85, 642)-Net over F₁₆ — Digital

Digital (45, 85, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (45, 86, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 43, 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]

(85−40, 85, 72553)-Net in Base 16 — Upper bound on s

There is no (45, 85, 72554)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 239878 993499 924552 099055 807650 825100 372917 089294 021229 493636 380626 422685 947037 131888 546707 554698 628076 > 16⁸⁵ [i]