MinT - Best Known (34, 75, s)-Nets in Base 9

Best Known (34, 75, s)-Nets in Base 9

(34, 75, 81)-Net over F₉ — Constructive and digital

Digital (34, 75, 81)-net over F₉, using

t-expansion [i] based on digital (32, 75, 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, 75, 88)-Net in Base 9 — Constructive

(34, 75, 88)-net in base 9, using

base change [i] based on digital (9, 50, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(34, 75, 128)-Net over F₉ — Digital

Digital (34, 75, 128)-net over F₉, using

t-expansion [i] based on digital (33, 75, 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, 75, 3511)-Net in Base 9 — Upper bound on s

There is no (34, 75, 3512)-net in base 9, because

1 times m-reduction [i] would yield (34, 74, 3512)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41339 273636 522018 866264 839801 221542 862626 534148 854008 913064 292544 574721 > 9⁷⁴ [i]