MinT - Best Known (36, 65, s)-Nets in Base 16

Best Known (36, 65, s)-Nets in Base 16

(36, 65, 520)-Net over F₁₆ — Constructive and digital

Digital (36, 65, 520)-net over F₁₆, using

1 times m-reduction [i] based on digital (36, 66, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(36, 65, 642)-Net over F₁₆ — Digital

Digital (36, 65, 642)-net over F₁₆, using

3 times m-reduction [i] based on digital (36, 68, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 34, 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]

(36, 65, 128792)-Net in Base 16 — Upper bound on s

There is no (36, 65, 128793)-net in base 16, because

1 times m-reduction [i] would yield (36, 64, 128793)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 115800 866092 967210 610019 568409 028675 044281 893440 682769 105109 925359 923987 865256 > 16⁶⁴ [i]