MinT - Best Known (78−36, 78, s)-Nets in Base 9

Best Known (78−36, 78, s)-Nets in Base 9

(78−36, 78, 232)-Net over F₉ — Constructive and digital

Digital (42, 78, 232)-net over F₉, using

2 times m-reduction [i] based on digital (42, 80, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 40, 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]

(78−36, 78, 272)-Net over F₉ — Digital

Digital (42, 78, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 39, 136)-net over F₈₁, using
- net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(78−36, 78, 12874)-Net in Base 9 — Upper bound on s

There is no (42, 78, 12875)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 269 930352 342576 966392 330079 905479 287828 231073 604359 555722 507316 941780 442801 > 9⁷⁸ [i]