MinT - Best Known (29, 29+105, s)-Nets in Base 9

Best Known (29, 29+105, s)-Nets in Base 9

(29, 29+105, 78)-Net over F₉ — Constructive and digital

Digital (29, 134, 78)-net over F₉, using

t-expansion [i] based on digital (22, 134, 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+105, 110)-Net over F₉ — Digital

Digital (29, 134, 110)-net over F₉, using

t-expansion [i] based on digital (26, 134, 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+105, 665)-Net in Base 9 — Upper bound on s

There is no (29, 134, 666)-net in base 9, because

1 times m-reduction [i] would yield (29, 133, 666)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 334599 507914 261714 873810 494453 104266 992013 056421 090347 200752 501506 054056 116498 466826 663198 899321 788663 034367 486259 943774 531265 > 9¹³³ [i]