MinT - Best Known (137−40, 137, s)-Nets in Base 3

Best Known (137−40, 137, s)-Nets in Base 3

(137−40, 137, 204)-Net over F₃ — Constructive and digital

Digital (97, 137, 204)-net over F₃, using

1 times m-reduction [i] based on digital (97, 138, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 46, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(137−40, 137, 354)-Net over F₃ — Digital

Digital (97, 137, 354)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−40, 137, 7681)-Net in Base 3 — Upper bound on s

There is no (97, 137, 7682)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 232251 443196 098386 897571 910503 468793 718517 173911 877485 377848 325577 > 3¹³⁷ [i]