MinT - Best Known (146−120, 146, s)-Nets in Base 9

Best Known (146−120, 146, s)-Nets in Base 9

(146−120, 146, 78)-Net over F₉ — Constructive and digital

Digital (26, 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]

(146−120, 146, 110)-Net over F₉ — Digital

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]

(146−120, 146, 572)-Net in Base 9 — Upper bound on s

There is no (26, 146, 573)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22 787431 247102 486193 792095 545609 253530 425547 732785 974677 667495 395186 941374 411101 811631 852510 522310 810667 892874 686588 899625 371416 913040 177633 > 9¹⁴⁶ [i]