MinT - Best Known (104−55, 104, s)-Nets in Base 9

Best Known (104−55, 104, s)-Nets in Base 9

(104−55, 104, 106)-Net over F₉ — Constructive and digital

Digital (49, 104, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 32, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 72, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(104−55, 104, 168)-Net over F₉ — Digital

Digital (49, 104, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(104−55, 104, 5948)-Net in Base 9 — Upper bound on s

There is no (49, 104, 5949)-net in base 9, because

1 times m-reduction [i] would yield (49, 103, 5949)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 194 374760 560485 430121 983693 595629 804587 591008 151142 871522 647026 826849 798790 338078 348382 282916 925625 > 9¹⁰³ [i]