MinT - Best Known (138, 138+41, s)-Nets in Base 3

Best Known (138, 138+41, s)-Nets in Base 3

(138, 138+41, 464)-Net over F₃ — Constructive and digital

Digital (138, 179, 464)-net over F₃, using

t-expansion [i] based on digital (137, 179, 464)-net over F₃, using
- 1 times m-reduction [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+41, 1096)-Net over F₃ — Digital

Digital (138, 179, 1096)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+41, 73204)-Net in Base 3 — Upper bound on s

There is no (138, 179, 73205)-net in base 3, because

1 times m-reduction [i] would yield (138, 178, 73205)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 464539 499356 286621 665520 697078 563599 383980 572897 978571 466718 327902 914498 786022 518161 > 3¹⁷⁸ [i]