MinT - Best Known (215−94, 215, s)-Nets in Base 3

Best Known (215−94, 215, s)-Nets in Base 3

(215−94, 215, 128)-Net over F₃ — Constructive and digital

Digital (121, 215, 128)-net over F₃, using

1 times m-reduction [i] based on digital (121, 216, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 108, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(215−94, 215, 155)-Net over F₃ — Digital

Digital (121, 215, 155)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−94, 215, 1352)-Net in Base 3 — Upper bound on s

There is no (121, 215, 1353)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 865713 961734 964731 350909 834324 279032 243393 674398 726581 974671 429596 774307 551008 042832 563985 589000 955147 > 3²¹⁵ [i]