MinT - Best Known (177−71, 177, s)-Nets in Base 3

Best Known (177−71, 177, s)-Nets in Base 3

(177−71, 177, 148)-Net over F₃ — Constructive and digital

Digital (106, 177, 148)-net over F₃, using

1 times m-reduction [i] based on digital (106, 178, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 89, 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]

(177−71, 177, 167)-Net over F₃ — Digital

Digital (106, 177, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−71, 177, 1709)-Net in Base 3 — Upper bound on s

There is no (106, 177, 1710)-net in base 3, because

1 times m-reduction [i] would yield (106, 176, 1710)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 950264 811421 016520 622287 783306 717322 083501 037002 389584 452766 850729 848125 395169 291009 > 3¹⁷⁶ [i]