MinT - Best Known (29, 29+103, s)-Nets in Base 9

Best Known (29, 29+103, s)-Nets in Base 9

(29, 29+103, 78)-Net over F₉ — Constructive and digital

Digital (29, 132, 78)-net over F₉, using

t-expansion [i] based on digital (22, 132, 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]

(29, 29+103, 110)-Net over F₉ — Digital

Digital (29, 132, 110)-net over F₉, using

t-expansion [i] based on digital (26, 132, 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]

(29, 29+103, 670)-Net in Base 9 — Upper bound on s

There is no (29, 132, 671)-net in base 9, because

1 times m-reduction [i] would yield (29, 131, 671)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106971 022400 690073 606652 334069 197315 698981 553199 253873 414961 951595 672573 723398 829256 932889 279737 775135 272017 709865 880887 456105 > 9¹³¹ [i]