MinT - Best Known (92−53, 92, s)-Nets in Base 9

Best Known (92−53, 92, s)-Nets in Base 9

(92−53, 92, 81)-Net over F₉ — Constructive and digital

Digital (39, 92, 81)-net over F₉, using

t-expansion [i] based on digital (32, 92, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(92−53, 92, 84)-Net in Base 9 — Constructive

(39, 92, 84)-net in base 9, using

1 times m-reduction [i] based on (39, 93, 84)-net in base 9, using
- base change [i] based on digital (8, 62, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(92−53, 92, 140)-Net over F₉ — Digital

Digital (39, 92, 140)-net over F₉, using

net from sequence [i] based on digital (39, 139)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
  - a curve from the manYPoints database [i]

(92−53, 92, 2868)-Net in Base 9 — Upper bound on s

There is no (39, 92, 2869)-net in base 9, because

1 times m-reduction [i] would yield (39, 91, 2869)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 687 754442 495603 400324 398203 749446 038916 296477 398916 342889 155839 949090 443365 175322 941393 > 9⁹¹ [i]