MinT - Best Known (136, 136+57, s)-Nets in Base 3

Best Known (136, 136+57, s)-Nets in Base 3

(136, 136+57, 246)-Net over F₃ — Constructive and digital

Digital (136, 193, 246)-net over F₃, using

3¹ times duplication [i] based on digital (135, 192, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 64, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(136, 136+57, 452)-Net over F₃ — Digital

Digital (136, 193, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+57, 10532)-Net in Base 3 — Upper bound on s

There is no (136, 193, 10533)-net in base 3, because

1 times m-reduction [i] would yield (136, 192, 10533)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 534993 020490 534399 126638 486858 138826 835773 438720 956125 966687 344802 585997 334000 667516 217585 > 3¹⁹² [i]