MinT - Best Known (27, 27+119, s)-Nets in Base 9

Best Known (27, 27+119, s)-Nets in Base 9

(27, 27+119, 78)-Net over F₉ — Constructive and digital

Digital (27, 146, 78)-net over F₉, using

t-expansion [i] based on digital (22, 146, 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]

(27, 27+119, 110)-Net over F₉ — Digital

Digital (27, 146, 110)-net over F₉, using

t-expansion [i] based on digital (26, 146, 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]

(27, 27+119, 595)-Net in Base 9 — Upper bound on s

There is no (27, 146, 596)-net in base 9, because

1 times m-reduction [i] would yield (27, 145, 596)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 363750 863598 189106 121470 970522 702646 731216 446992 301045 083579 587784 662027 991682 645798 514827 337586 536624 109211 968596 399063 722545 476193 627745 > 9¹⁴⁵ [i]