MinT - Best Known (84−46, 84, s)-Nets in Base 9

Best Known (84−46, 84, s)-Nets in Base 9

(84−46, 84, 84)-Net over F₉ — Constructive and digital

Digital (38, 84, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 25, 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, 59, 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]

(84−46, 84, 94)-Net in Base 9 — Constructive

(38, 84, 94)-net in base 9, using

base change [i] based on digital (10, 56, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(84−46, 84, 128)-Net over F₉ — Digital

Digital (38, 84, 128)-net over F₉, using

t-expansion [i] based on digital (33, 84, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(84−46, 84, 3587)-Net in Base 9 — Upper bound on s

There is no (38, 84, 3588)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 144 108519 403669 384361 368503 993688 639953 994902 506177 207553 376849 806820 926390 293345 > 9⁸⁴ [i]