MinT - Best Known (128−76, 128, s)-Nets in Base 9

Best Known (128−76, 128, s)-Nets in Base 9

(128−76, 128, 81)-Net over F₉ — Constructive and digital

Digital (52, 128, 81)-net over F₉, using

t-expansion [i] based on digital (32, 128, 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]

(128−76, 128, 88)-Net in Base 9 — Constructive

(52, 128, 88)-net in base 9, using

1 times m-reduction [i] based on (52, 129, 88)-net in base 9, using
- base change [i] based on digital (9, 86, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(128−76, 128, 182)-Net over F₉ — Digital

Digital (52, 128, 182)-net over F₉, using

t-expansion [i] based on digital (50, 128, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(128−76, 128, 3052)-Net in Base 9 — Upper bound on s

There is no (52, 128, 3053)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 137573 196097 659142 637893 289377 108695 490102 898902 780443 723287 671448 538620 956842 113680 146874 686570 276592 890434 911253 800625 > 9¹²⁸ [i]