MinT - Best Known (178−43, 178, s)-Nets in Base 3

Best Known (178−43, 178, s)-Nets in Base 3

(178−43, 178, 400)-Net over F₃ — Constructive and digital

Digital (135, 178, 400)-net over F₃, using

3² 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]

(178−43, 178, 889)-Net over F₃ — Digital

Digital (135, 178, 889)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−43, 178, 45574)-Net in Base 3 — Upper bound on s

There is no (135, 178, 45575)-net in base 3, because

1 times m-reduction [i] would yield (135, 177, 45575)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 822583 896993 837764 077100 937463 160305 034996 529691 320088 563261 845559 250554 305812 869671 > 3¹⁷⁷ [i]