MinT - Best Known (177−43, 177, s)-Nets in Base 3

Best Known (177−43, 177, s)-Nets in Base 3

(177−43, 177, 400)-Net over F₃ — Constructive and digital

Digital (134, 177, 400)-net over F₃, using

3¹ times duplication [i] based on digital (133, 176, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 44, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(177−43, 177, 866)-Net over F₃ — Digital

Digital (134, 177, 866)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−43, 177, 43250)-Net in Base 3 — Upper bound on s

There is no (134, 177, 43251)-net in base 3, because

1 times m-reduction [i] would yield (134, 176, 43251)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 940862 362176 347669 592469 854916 113970 077058 658546 964276 582600 117066 734743 018643 747903 > 3¹⁷⁶ [i]