MinT - Best Known (179−55, 179, s)-Nets in Base 3

Best Known (179−55, 179, s)-Nets in Base 3

(179−55, 179, 192)-Net over F₃ — Constructive and digital

Digital (124, 179, 192)-net over F₃, using

1 times m-reduction [i] based on digital (124, 180, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 60, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(179−55, 179, 373)-Net over F₃ — Digital

Digital (124, 179, 373)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−55, 179, 7609)-Net in Base 3 — Upper bound on s

There is no (124, 179, 7610)-net in base 3, because

1 times m-reduction [i] would yield (124, 178, 7610)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 490158 318336 059956 086524 067129 369824 638233 892623 282308 883700 650559 068112 920381 191681 > 3¹⁷⁸ [i]