MinT - Best Known (138, 138+44, s)-Nets in Base 3

Best Known (138, 138+44, s)-Nets in Base 3

(138, 138+44, 400)-Net over F₃ — Constructive and digital

Digital (138, 182, 400)-net over F₃, using

3² times duplication [i] based on digital (136, 180, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 45, 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]

(138, 138+44, 903)-Net over F₃ — Digital

Digital (138, 182, 903)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+44, 40057)-Net in Base 3 — Upper bound on s

There is no (138, 182, 40058)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 776583 935409 346173 099001 006681 428882 048758 301870 070356 972197 051020 695081 725967 640109 > 3¹⁸² [i]