MinT - Best Known (89−30, 89, s)-Nets in Base 9

Best Known (89−30, 89, s)-Nets in Base 9

(89−30, 89, 448)-Net over F₉ — Constructive and digital

Digital (59, 89, 448)-net over F₉, using

3 times m-reduction [i] based on digital (59, 92, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 46, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(89−30, 89, 1252)-Net over F₉ — Digital

Digital (59, 89, 1252)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−30, 89, 368557)-Net in Base 9 — Upper bound on s

There is no (59, 89, 368558)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 464371 144421 627417 444197 803325 087769 046715 036001 637918 172055 211324 778115 090735 792593 > 9⁸⁹ [i]