MinT - Best Known (180−47, 180, s)-Nets in Base 3

Best Known (180−47, 180, s)-Nets in Base 3

(180−47, 180, 288)-Net over F₃ — Constructive and digital

Digital (133, 180, 288)-net over F₃, using

3 times m-reduction [i] based on digital (133, 183, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 61, 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]

(180−47, 180, 659)-Net over F₃ — Digital

Digital (133, 180, 659)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−47, 180, 24337)-Net in Base 3 — Upper bound on s

There is no (133, 180, 24338)-net in base 3, because

1 times m-reduction [i] would yield (133, 179, 24338)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 408232 950828 930526 695206 001210 576537 025983 511395 604025 463873 110521 116790 915418 291849 > 3¹⁷⁹ [i]