MinT - Best Known (27−12, 27, s)-Nets in Base 16

Best Known (27−12, 27, s)-Nets in Base 16

(27−12, 27, 516)-Net over F₁₆ — Constructive and digital

Digital (15, 27, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (15, 28, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 14, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(27−12, 27, 578)-Net over F₁₆ — Digital

Digital (15, 27, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (15, 28, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 14, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(27−12, 27, 52317)-Net in Base 16 — Upper bound on s

There is no (15, 27, 52318)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 324 538549 648302 365995 657513 441996 > 16²⁷ [i]