MinT - Best Known (136, 136+101, s)-Nets in Base 3

Best Known (136, 136+101, s)-Nets in Base 3

(136, 136+101, 148)-Net over F₃ — Constructive and digital

Digital (136, 237, 148)-net over F₃, using

1 times m-reduction [i] based on digital (136, 238, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 119, 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]

(136, 136+101, 182)-Net over F₃ — Digital

Digital (136, 237, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+101, 1691)-Net in Base 3 — Upper bound on s

There is no (136, 237, 1692)-net in base 3, because

1 times m-reduction [i] would yield (136, 236, 1692)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40493 859820 251500 121758 431277 082624 987561 223648 597009 688633 150506 480824 931549 526528 534475 998355 424376 512313 289417 > 3²³⁶ [i]