MinT - Best Known (30, 30+61, s)-Nets in Base 9

Best Known (30, 30+61, s)-Nets in Base 9

(30, 30+61, 78)-Net over F₉ — Constructive and digital

Digital (30, 91, 78)-net over F₉, using

t-expansion [i] based on digital (22, 91, 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+61, 110)-Net over F₉ — Digital

Digital (30, 91, 110)-net over F₉, using

t-expansion [i] based on digital (26, 91, 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+61, 1079)-Net in Base 9 — Upper bound on s

There is no (30, 91, 1080)-net in base 9, because

1 times m-reduction [i] would yield (30, 90, 1080)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77 449261 749047 273706 281607 199167 001762 003048 974783 099203 013467 380521 925345 569659 359617 > 9⁹⁰ [i]