MinT - Best Known (34, 34+51, s)-Nets in Base 9

Best Known (34, 34+51, s)-Nets in Base 9

(34, 34+51, 81)-Net over F₉ — Constructive and digital

Digital (34, 85, 81)-net over F₉, using

t-expansion [i] based on digital (32, 85, 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+51, 128)-Net over F₉ — Digital

Digital (34, 85, 128)-net over F₉, using

t-expansion [i] based on digital (33, 85, 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+51, 2030)-Net in Base 9 — Upper bound on s

There is no (34, 85, 2031)-net in base 9, because

1 times m-reduction [i] would yield (34, 84, 2031)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 144 454711 068873 613443 028103 028404 041146 941183 884644 906887 094398 463702 598804 490937 > 9⁸⁴ [i]