MinT - Best Known (25, 25+122, s)-Nets in Base 9

Best Known (25, 25+122, s)-Nets in Base 9

(25, 25+122, 78)-Net over F₉ — Constructive and digital

Digital (25, 147, 78)-net over F₉, using

t-expansion [i] based on digital (22, 147, 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]

(25, 25+122, 96)-Net over F₉ — Digital

Digital (25, 147, 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]

(25, 25+122, 550)-Net in Base 9 — Upper bound on s

There is no (25, 147, 551)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 205 277854 178106 239291 595690 446069 260735 795039 815520 792877 742088 356484 964475 546639 326444 324585 454344 242152 407085 501805 433378 283540 700073 172057 > 9¹⁴⁷ [i]