MinT - Best Known (179−47, 179, s)-Nets in Base 3

Best Known (179−47, 179, s)-Nets in Base 3

(179−47, 179, 288)-Net over F₃ — Constructive and digital

Digital (132, 179, 288)-net over F₃, using

t-expansion [i] based on digital (131, 179, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (131, 180, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 60, 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]

(179−47, 179, 642)-Net over F₃ — Digital

Digital (132, 179, 642)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−47, 179, 23201)-Net in Base 3 — Upper bound on s

There is no (132, 179, 23202)-net in base 3, because

1 times m-reduction [i] would yield (132, 178, 23202)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 471457 335508 953212 416602 028530 908983 072302 851904 087669 585028 910307 137753 423750 481481 > 3¹⁷⁸ [i]