MinT - Best Known (177−45, 177, s)-Nets in Base 3

Best Known (177−45, 177, s)-Nets in Base 3

(177−45, 177, 288)-Net over F₃ — Constructive and digital

Digital (132, 177, 288)-net over F₃, using

t-expansion [i] based on digital (131, 177, 288)-net over F₃, using
- 3 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]

(177−45, 177, 721)-Net over F₃ — Digital

Digital (132, 177, 721)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−45, 177, 29681)-Net in Base 3 — Upper bound on s

There is no (132, 177, 29682)-net in base 3, because

1 times m-reduction [i] would yield (132, 176, 29682)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 941150 302662 295072 902068 804445 379861 083929 635541 717981 644707 411657 559165 690604 952957 > 3¹⁷⁶ [i]