MinT - Best Known (128, 128+93, s)-Nets in Base 3

Best Known (128, 128+93, s)-Nets in Base 3

(128, 128+93, 148)-Net over F₃ — Constructive and digital

Digital (128, 221, 148)-net over F₃, using

1 times m-reduction [i] based on digital (128, 222, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 111, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(128, 128+93, 177)-Net over F₃ — Digital

Digital (128, 221, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+93, 1677)-Net in Base 3 — Upper bound on s

There is no (128, 221, 1678)-net in base 3, because

1 times m-reduction [i] would yield (128, 220, 1678)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 946 237626 658741 394311 131178 378576 602645 346413 304269 596602 724874 140237 236811 604981 170990 327513 793858 499029 > 3²²⁰ [i]