MinT - Best Known (83−49, 83, s)-Nets in Base 9

Best Known (83−49, 83, s)-Nets in Base 9

(83−49, 83, 81)-Net over F₉ — Constructive and digital

Digital (34, 83, 81)-net over F₉, using

t-expansion [i] based on digital (32, 83, 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]

(83−49, 83, 128)-Net over F₉ — Digital

Digital (34, 83, 128)-net over F₉, using

t-expansion [i] based on digital (33, 83, 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]

(83−49, 83, 2217)-Net in Base 9 — Upper bound on s

There is no (34, 83, 2218)-net in base 9, because

1 times m-reduction [i] would yield (34, 82, 2218)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 787797 380173 658566 462305 538300 618220 611011 604491 367788 562038 246657 073700 487809 > 9⁸² [i]