MinT - Best Known (53, 130, s)-Nets in Base 9

Best Known (53, 130, s)-Nets in Base 9

(53, 130, 84)-Net over F₉ — Constructive and digital

Digital (53, 130, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 40, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 90, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(53, 130, 88)-Net in Base 9 — Constructive

(53, 130, 88)-net in base 9, using

2 times m-reduction [i] based on (53, 132, 88)-net in base 9, using
- base change [i] based on digital (9, 88, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(53, 130, 182)-Net over F₉ — Digital

Digital (53, 130, 182)-net over F₉, using

t-expansion [i] based on digital (50, 130, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(53, 130, 3236)-Net in Base 9 — Upper bound on s

There is no (53, 130, 3237)-net in base 9, because

1 times m-reduction [i] would yield (53, 129, 3237)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1265 281696 085371 478030 889227 555500 894385 607354 613985 360638 797121 531997 691550 326391 112251 893288 997145 016676 027951 804025 195569 > 9¹²⁹ [i]