MinT - Best Known (43, 43+37, s)-Nets in Base 9

Best Known (43, 43+37, s)-Nets in Base 9

(43, 43+37, 232)-Net over F₉ — Constructive and digital

Digital (43, 80, 232)-net over F₉, using

2 times m-reduction [i] based on digital (43, 82, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 41, 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]

(43, 43+37, 272)-Net over F₉ — Digital

Digital (43, 80, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 40, 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]

(43, 43+37, 14547)-Net in Base 9 — Upper bound on s

There is no (43, 80, 14548)-net in base 9, because

1 times m-reduction [i] would yield (43, 79, 14548)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2429 467248 226151 982817 550482 012476 226983 682148 869993 341228 029749 760582 791105 > 9⁷⁹ [i]