MinT - Best Known (177, 177+67, s)-Nets in Base 3

Best Known (177, 177+67, s)-Nets in Base 3

(177, 177+67, 288)-Net over F₃ — Constructive and digital

Digital (177, 244, 288)-net over F₃, using

5 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 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, 177+67, 708)-Net over F₃ — Digital

Digital (177, 244, 708)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+67, 21429)-Net in Base 3 — Upper bound on s

There is no (177, 244, 21430)-net in base 3, because

1 times m-reduction [i] would yield (177, 243, 21430)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 245014 726099 041309 351130 662192 545628 769205 126628 459558 653722 244739 714874 447814 640466 649078 333505 990803 429034 237741 > 3²⁴³ [i]