MinT - Best Known (92−55, 92, s)-Nets in Base 9

Best Known (92−55, 92, s)-Nets in Base 9

(92−55, 92, 81)-Net over F₉ — Constructive and digital

Digital (37, 92, 81)-net over F₉, using

t-expansion [i] based on digital (32, 92, 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]

(92−55, 92, 128)-Net over F₉ — Digital

Digital (37, 92, 128)-net over F₉, using

t-expansion [i] based on digital (33, 92, 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]

(92−55, 92, 2229)-Net in Base 9 — Upper bound on s

There is no (37, 92, 2230)-net in base 9, because

1 times m-reduction [i] would yield (37, 91, 2230)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 935283 356142 592893 755575 371223 874789 621661 873945 866161 143792 917378 267203 546965 122641 > 9⁹¹ [i]