MinT - Best Known (128−98, 128, s)-Nets in Base 9

Best Known (128−98, 128, s)-Nets in Base 9

(128−98, 128, 78)-Net over F₉ — Constructive and digital

Digital (30, 128, 78)-net over F₉, using

t-expansion [i] based on digital (22, 128, 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]

(128−98, 128, 110)-Net over F₉ — Digital

Digital (30, 128, 110)-net over F₉, using

t-expansion [i] based on digital (26, 128, 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]

(128−98, 128, 713)-Net in Base 9 — Upper bound on s

There is no (30, 128, 714)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 147 200406 569107 859485 520413 352974 472507 832887 625654 902804 607598 210390 635675 036258 335665 877105 620848 218782 782179 232299 855697 > 9¹²⁸ [i]