MinT - Best Known (83−48, 83, s)-Nets in Base 9

Best Known (83−48, 83, s)-Nets in Base 9

(83−48, 83, 81)-Net over F₉ — Constructive and digital

Digital (35, 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]

(83−48, 83, 82)-Net in Base 9 — Constructive

(35, 83, 82)-net in base 9, using

1 times m-reduction [i] based on (35, 84, 82)-net in base 9, using
- base change [i] based on digital (7, 56, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(83−48, 83, 128)-Net over F₉ — Digital

Digital (35, 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]

(83−48, 83, 2430)-Net in Base 9 — Upper bound on s

There is no (35, 83, 2431)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 928279 938035 344085 123873 638274 591233 979874 714553 176216 446381 881738 049641 471809 > 9⁸³ [i]