MinT - Best Known (109−84, 109, s)-Nets in Base 9

Best Known (109−84, 109, s)-Nets in Base 9

(109−84, 109, 78)-Net over F₉ — Constructive and digital

Digital (25, 109, 78)-net over F₉, using

t-expansion [i] based on digital (22, 109, 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]

(109−84, 109, 96)-Net over F₉ — Digital

Digital (25, 109, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(109−84, 109, 592)-Net in Base 9 — Upper bound on s

There is no (25, 109, 593)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103 899832 322544 149747 483051 240160 681065 401849 291374 598702 866451 368479 250380 311904 308357 365331 174899 677073 > 9¹⁰⁹ [i]