MinT - Best Known (44, 44+59, s)-Nets in Base 9

Best Known (44, 44+59, s)-Nets in Base 9

(44, 44+59, 84)-Net over F₉ — Constructive and digital

Digital (44, 103, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 31, 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, 72, 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]

(44, 44+59, 88)-Net in Base 9 — Constructive

(44, 103, 88)-net in base 9, using

2 times m-reduction [i] based on (44, 105, 88)-net in base 9, using
- base change [i] based on digital (9, 70, 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]

(44, 44+59, 147)-Net over F₉ — Digital

Digital (44, 103, 147)-net over F₉, using

t-expansion [i] based on digital (43, 103, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(44, 44+59, 3296)-Net in Base 9 — Upper bound on s

There is no (44, 103, 3297)-net in base 9, because

1 times m-reduction [i] would yield (44, 102, 3297)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 655244 860905 766904 741937 811296 630153 567515 676019 444522 230329 729046 825867 594411 069304 958293 804393 > 9¹⁰² [i]