MinT - Best Known (138, 138+43, s)-Nets in Base 3

Best Known (138, 138+43, s)-Nets in Base 3

(138, 138+43, 464)-Net over F₃ — Constructive and digital

Digital (138, 181, 464)-net over F₃, using

3¹ times duplication [i] based on digital (137, 180, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 45, 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]

(138, 138+43, 960)-Net over F₃ — Digital

Digital (138, 181, 960)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+43, 53321)-Net in Base 3 — Upper bound on s

There is no (138, 181, 53322)-net in base 3, because

1 times m-reduction [i] would yield (138, 180, 53322)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 177395 044212 106761 781355 134143 833044 410024 515395 234562 807170 008816 527774 862814 013005 > 3¹⁸⁰ [i]