MinT - Best Known (124−47, 124, s)-Nets in Base 3

Best Known (124−47, 124, s)-Nets in Base 3

(124−47, 124, 128)-Net over F₃ — Constructive and digital

Digital (77, 124, 128)-net over F₃, using

4 times m-reduction [i] based on digital (77, 128, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 64, 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]

(124−47, 124, 146)-Net over F₃ — Digital

Digital (77, 124, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−47, 124, 1656)-Net in Base 3 — Upper bound on s

There is no (77, 124, 1657)-net in base 3, because

1 times m-reduction [i] would yield (77, 123, 1657)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48931 807221 700691 917142 530402 665962 250967 745843 779734 174507 > 3¹²³ [i]