MinT - Best Known (28, 28+109, s)-Nets in Base 9

Best Known (28, 28+109, s)-Nets in Base 9

(28, 28+109, 78)-Net over F₉ — Constructive and digital

Digital (28, 137, 78)-net over F₉, using

t-expansion [i] based on digital (22, 137, 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, 28+109, 110)-Net over F₉ — Digital

Digital (28, 137, 110)-net over F₉, using

t-expansion [i] based on digital (26, 137, 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, 28+109, 630)-Net in Base 9 — Upper bound on s

There is no (28, 137, 631)-net in base 9, because

1 times m-reduction [i] would yield (28, 136, 631)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6203 120509 465732 140730 236931 380296 541153 292285 852141 229207 896719 767728 549656 053138 059137 599695 343687 263713 823614 337256 474806 929361 > 9¹³⁶ [i]