MinT - Best Known (104−75, 104, s)-Nets in Base 9

Best Known (104−75, 104, s)-Nets in Base 9

(104−75, 104, 78)-Net over F₉ — Constructive and digital

Digital (29, 104, 78)-net over F₉, using

t-expansion [i] based on digital (22, 104, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(104−75, 104, 110)-Net over F₉ — Digital

Digital (29, 104, 110)-net over F₉, using

t-expansion [i] based on digital (26, 104, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(104−75, 104, 807)-Net in Base 9 — Upper bound on s

There is no (29, 104, 808)-net in base 9, because

1 times m-reduction [i] would yield (29, 103, 808)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 195 031619 369281 918493 379288 158213 127314 942844 621002 454719 545110 851371 972847 162500 801987 617903 032385 > 9¹⁰³ [i]