MinT - Best Known (121, 121+55, s)-Nets in Base 3

Best Known (121, 121+55, s)-Nets in Base 3

(121, 121+55, 162)-Net over F₃ — Constructive and digital

Digital (121, 176, 162)-net over F₃, using

2 times m-reduction [i] based on digital (121, 178, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 89, 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]

(121, 121+55, 349)-Net over F₃ — Digital

Digital (121, 176, 349)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+55, 6731)-Net in Base 3 — Upper bound on s

There is no (121, 176, 6732)-net in base 3, because

1 times m-reduction [i] would yield (121, 175, 6732)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313841 579024 198033 263936 204848 139495 029495 051389 585964 077679 744741 233316 207913 623441 > 3¹⁷⁵ [i]