MinT - Best Known (30, 30+119, s)-Nets in Base 9

Best Known (30, 30+119, s)-Nets in Base 9

(30, 30+119, 78)-Net over F₉ — Constructive and digital

Digital (30, 149, 78)-net over F₉, using

t-expansion [i] based on digital (22, 149, 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]

(30, 30+119, 110)-Net over F₉ — Digital

Digital (30, 149, 110)-net over F₉, using

t-expansion [i] based on digital (26, 149, 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]

(30, 30+119, 670)-Net in Base 9 — Upper bound on s

There is no (30, 149, 671)-net in base 9, because

1 times m-reduction [i] would yield (30, 148, 671)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1779 286869 838784 417414 700796 921020 860223 071983 529705 887782 989814 985646 234044 076362 186502 934146 048610 013010 268881 627940 973647 353660 423977 863465 > 9¹⁴⁸ [i]