MinT - Best Known (167, 167+71, s)-Nets in Base 3

Best Known (167, 167+71, s)-Nets in Base 3

(167, 167+71, 252)-Net over F₃ — Constructive and digital

Digital (167, 238, 252)-net over F₃, using

3¹ times duplication [i] based on digital (166, 237, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 79, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(167, 167+71, 525)-Net over F₃ — Digital

Digital (167, 238, 525)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+71, 11796)-Net in Base 3 — Upper bound on s

There is no (167, 238, 11797)-net in base 3, because

1 times m-reduction [i] would yield (167, 237, 11797)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119717 207320 868917 604423 140308 511056 330294 052540 550131 172276 042436 682771 035622 234693 005468 425543 957110 826530 963755 > 3²³⁷ [i]