MinT - Best Known (56−26, 56, s)-Nets in Base 9

Best Known (56−26, 56, s)-Nets in Base 9

(56−26, 56, 232)-Net over F₉ — Constructive and digital

Digital (30, 56, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 28, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(56−26, 56, 236)-Net over F₉ — Digital

Digital (30, 56, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 28, 118)-net over F₈₁, using
- net from sequence [i] based on digital (2, 117)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(56−26, 56, 9131)-Net in Base 9 — Upper bound on s

There is no (30, 56, 9132)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274130 400530 292651 531467 401177 924773 987373 758483 187425 > 9⁵⁶ [i]