MinT - Best Known (171, 171+67, s)-Nets in Base 3

Best Known (171, 171+67, s)-Nets in Base 3

(171, 171+67, 288)-Net over F₃ — Constructive and digital

Digital (171, 238, 288)-net over F₃, using

2 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 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]

(171, 171+67, 636)-Net over F₃ — Digital

Digital (171, 238, 636)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+67, 17543)-Net in Base 3 — Upper bound on s

There is no (171, 238, 17544)-net in base 3, because

1 times m-reduction [i] would yield (171, 237, 17544)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119688 622291 482301 569425 144801 769102 640180 999747 000978 128425 966710 769611 085428 944827 590906 716188 558676 990811 403025 > 3²³⁷ [i]