MinT - Best Known (53, 53+47, s)-Nets in Base 9

Best Known (53, 53+47, s)-Nets in Base 9

(53, 53+47, 232)-Net over F₉ — Constructive and digital

Digital (53, 100, 232)-net over F₉, using

2 times m-reduction [i] based on digital (53, 102, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 51, 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]

(53, 53+47, 272)-Net over F₉ — Digital

Digital (53, 100, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 50, 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]

(53, 53+47, 15078)-Net in Base 9 — Upper bound on s

There is no (53, 100, 15079)-net in base 9, because

1 times m-reduction [i] would yield (53, 99, 15079)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29534 401757 435459 720789 091581 902684 602659 219486 436772 299557 541323 175352 246537 655717 472706 645257 > 9⁹⁹ [i]