MinT - Best Known (150−120, 150, s)-Nets in Base 9

Best Known (150−120, 150, s)-Nets in Base 9

(150−120, 150, 78)-Net over F₉ — Constructive and digital

Digital (30, 150, 78)-net over F₉, using

t-expansion [i] based on digital (22, 150, 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]

(150−120, 150, 110)-Net over F₉ — Digital

Digital (30, 150, 110)-net over F₉, using

t-expansion [i] based on digital (26, 150, 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]

(150−120, 150, 668)-Net in Base 9 — Upper bound on s

There is no (30, 150, 669)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 148955 327343 452252 314225 890934 624133 881970 176263 463228 290584 209011 067254 034055 189477 545376 326949 054868 906211 818723 437478 402378 536293 730795 378145 > 9¹⁵⁰ [i]