MinT - Best Known (33, 33+57, s)-Nets in Base 9

Best Known (33, 33+57, s)-Nets in Base 9

(33, 33+57, 81)-Net over F₉ — Constructive and digital

Digital (33, 90, 81)-net over F₉, using

t-expansion [i] based on digital (32, 90, 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]

(33, 33+57, 128)-Net over F₉ — Digital

Digital (33, 90, 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]

(33, 33+57, 1507)-Net in Base 9 — Upper bound on s

There is no (33, 90, 1508)-net in base 9, because

1 times m-reduction [i] would yield (33, 89, 1508)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 580010 787322 628718 139799 077699 375287 205489 159742 599097 886247 319340 812107 868599 525505 > 9⁸⁹ [i]