MinT - Best Known (29, 126, s)-Nets in Base 9

Best Known (29, 126, s)-Nets in Base 9

(29, 126, 78)-Net over F₉ — Constructive and digital

Digital (29, 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]

(29, 126, 110)-Net over F₉ — Digital

Digital (29, 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]

(29, 126, 686)-Net in Base 9 — Upper bound on s

There is no (29, 126, 687)-net in base 9, because

1 times m-reduction [i] would yield (29, 125, 687)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 197064 823154 366031 898601 835483 908506 586675 934262 801298 273136 471478 848392 742701 092538 150924 014089 719806 002254 551802 451585 > 9¹²⁵ [i]