MinT - Best Known (164−43, 164, s)-Nets in Base 3

Best Known (164−43, 164, s)-Nets in Base 3

(164−43, 164, 288)-Net over F₃ — Constructive and digital

Digital (121, 164, 288)-net over F₃, using

1 times m-reduction [i] based on digital (121, 165, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 55, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(164−43, 164, 602)-Net over F₃ — Digital

Digital (121, 164, 602)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−43, 164, 21899)-Net in Base 3 — Upper bound on s

There is no (121, 164, 21900)-net in base 3, because

1 times m-reduction [i] would yield (121, 163, 21900)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590394 412645 013637 614778 012468 531974 091716 007887 803437 776712 417820 279026 120441 > 3¹⁶³ [i]