MinT - Best Known (98−54, 98, s)-Nets in Base 9

Best Known (98−54, 98, s)-Nets in Base 9

(98−54, 98, 94)-Net over F₉ — Constructive and digital

Digital (44, 98, 94)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 31, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]
2. digital (13, 67, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(98−54, 98, 96)-Net in Base 9 — Constructive

(44, 98, 96)-net in base 9, using

1 times m-reduction [i] based on (44, 99, 96)-net in base 9, using
- base change [i] based on digital (11, 66, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(98−54, 98, 147)-Net over F₉ — Digital

Digital (44, 98, 147)-net over F₉, using

t-expansion [i] based on digital (43, 98, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(98−54, 98, 3954)-Net in Base 9 — Upper bound on s

There is no (44, 98, 3955)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3294 518406 476439 317349 288050 195483 912815 378243 613689 260042 853213 471461 238333 299465 143236 741513 > 9⁹⁸ [i]