MinT - Best Known (223−57, 223, s)-Nets in Base 3

Best Known (223−57, 223, s)-Nets in Base 3

(223−57, 223, 288)-Net over F₃ — Constructive and digital

Digital (166, 223, 288)-net over F₃, using

t-expansion [i] based on digital (165, 223, 288)-net over F₃, using
- 8 times m-reduction [i] based on digital (165, 231, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 77, 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]

(223−57, 223, 853)-Net over F₃ — Digital

Digital (166, 223, 853)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−57, 223, 34238)-Net in Base 3 — Upper bound on s

There is no (166, 223, 34239)-net in base 3, because

1 times m-reduction [i] would yield (166, 222, 34239)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8337 747078 858226 728876 133164 744506 676534 715377 602282 576422 355304 919026 757535 937547 762053 123837 566067 246025 > 3²²² [i]