MinT - Best Known (129−107, 129, s)-Nets in Base 9

Best Known (129−107, 129, s)-Nets in Base 9

(129−107, 129, 78)-Net over F₉ — Constructive and digital

Digital (22, 129, 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]

(129−107, 129, 88)-Net over F₉ — Digital

Digital (22, 129, 88)-net over F₉, using

t-expansion [i] based on digital (21, 129, 88)-net over F₉, using
- net from sequence [i] based on digital (21, 87)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
    - a curve from the manYPoints database [i]

(129−107, 129, 487)-Net in Base 9 — Upper bound on s

There is no (22, 129, 488)-net in base 9, because

1 times m-reduction [i] would yield (22, 128, 488)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 152 360735 685384 270296 480154 970674 728333 698119 835260 287723 972504 244988 280840 551058 664724 660719 128114 606251 336082 297429 332545 > 9¹²⁸ [i]