MinT - Best Known (126−98, 126, s)-Nets in Base 9

Best Known (126−98, 126, s)-Nets in Base 9

(126−98, 126, 78)-Net over F₉ — Constructive and digital

Digital (28, 126, 78)-net over F₉, using

t-expansion [i] based on digital (22, 126, 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]

(126−98, 126, 110)-Net over F₉ — Digital

Digital (28, 126, 110)-net over F₉, using

t-expansion [i] based on digital (26, 126, 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]

(126−98, 126, 649)-Net in Base 9 — Upper bound on s

There is no (28, 126, 650)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 787083 778417 149623 825127 437722 468563 712414 306744 204097 792096 955482 356393 504948 624836 448297 996727 136714 436517 374190 390609 > 9¹²⁶ [i]