MinT - Best Known (34, 34+43, s)-Nets in Base 9

Best Known (34, 34+43, s)-Nets in Base 9

(34, 34+43, 81)-Net over F₉ — Constructive and digital

Digital (34, 77, 81)-net over F₉, using

t-expansion [i] based on digital (32, 77, 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+43, 84)-Net in Base 9 — Constructive

(34, 77, 84)-net in base 9, using

1 times m-reduction [i] based on (34, 78, 84)-net in base 9, using
- base change [i] based on digital (8, 52, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(34, 34+43, 128)-Net over F₉ — Digital

Digital (34, 77, 128)-net over F₉, using

t-expansion [i] based on digital (33, 77, 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+43, 3069)-Net in Base 9 — Upper bound on s

There is no (34, 77, 3070)-net in base 9, because

1 times m-reduction [i] would yield (34, 76, 3070)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 340677 632094 945263 155290 357739 566945 822040 839957 734869 945177 319302 173489 > 9⁷⁶ [i]