MinT - Best Known (34, 34+47, s)-Nets in Base 9

Best Known (34, 34+47, s)-Nets in Base 9

(34, 34+47, 81)-Net over F₉ — Constructive and digital

Digital (34, 81, 81)-net over F₉, using

t-expansion [i] based on digital (32, 81, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(34, 34+47, 82)-Net in Base 9 — Constructive

(34, 81, 82)-net in base 9, using

base change [i] based on digital (7, 54, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(34, 34+47, 128)-Net over F₉ — Digital

Digital (34, 81, 128)-net over F₉, using

t-expansion [i] based on digital (33, 81, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(34, 34+47, 2443)-Net in Base 9 — Upper bound on s

There is no (34, 81, 2444)-net in base 9, because

1 times m-reduction [i] would yield (34, 80, 2444)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21946 006206 673141 095048 391895 182369 693268 635884 712112 404863 925588 363519 756833 > 9⁸⁰ [i]