MinT - Best Known (28, 138, s)-Nets in Base 9

Best Known (28, 138, s)-Nets in Base 9

(28, 138, 78)-Net over F₉ — Constructive and digital

Digital (28, 138, 78)-net over F₉, using

t-expansion [i] based on digital (22, 138, 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]

(28, 138, 110)-Net over F₉ — Digital

Digital (28, 138, 110)-net over F₉, using

t-expansion [i] based on digital (26, 138, 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]

(28, 138, 627)-Net in Base 9 — Upper bound on s

There is no (28, 138, 628)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 490946 679406 728700 053189 806449 525985 773420 914575 835456 861750 050870 968302 736100 414534 187136 346988 879717 346559 247375 616682 297409 349089 > 9¹³⁸ [i]