MinT - Best Known (51, 51+46, s)-Nets in Base 9

Best Known (51, 51+46, s)-Nets in Base 9

(51, 51+46, 232)-Net over F₉ — Constructive and digital

Digital (51, 97, 232)-net over F₉, using

1 times m-reduction [i] based on digital (51, 98, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 49, 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]

(51, 51+46, 241)-Net over F₉ — Digital

Digital (51, 97, 241)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+46, 12453)-Net in Base 9 — Upper bound on s

There is no (51, 97, 12454)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 584064 614103 370892 288139 473155 569646 606257 234493 301719 062336 586891 601547 157257 977496 685457 > 9⁹⁷ [i]