MinT - Best Known (135, 135+42, s)-Nets in Base 3

Best Known (135, 135+42, s)-Nets in Base 3

(135, 135+42, 464)-Net over F₃ — Constructive and digital

Digital (135, 177, 464)-net over F₃, using

3¹ times duplication [i] based on digital (134, 176, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 44, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(135, 135+42, 946)-Net over F₃ — Digital

Digital (135, 177, 946)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+42, 45574)-Net in Base 3 — Upper bound on s

There is no (135, 177, 45575)-net in base 3, because

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]