MinT - Best Known (76−41, 76, s)-Nets in Base 8

Best Known (76−41, 76, s)-Nets in Base 8

(76−41, 76, 79)-Net over F₈ — Constructive and digital

Digital (35, 76, 79)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 21, 14)-net over F₈, using
  - net from sequence [i] based on digital (1, 13)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. digital (14, 55, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(76−41, 76, 112)-Net over F₈ — Digital

Digital (35, 76, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(76−41, 76, 2876)-Net in Base 8 — Upper bound on s

There is no (35, 76, 2877)-net in base 8, because

1 times m-reduction [i] would yield (35, 75, 2877)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 927617 219509 317356 568342 884744 695088 265048 741675 683448 795004 646631 > 8⁷⁵ [i]