MinT - Best Known (230−60, 230, s)-Nets in Base 3

Best Known (230−60, 230, s)-Nets in Base 3

(230−60, 230, 288)-Net over F₃ — Constructive and digital

Digital (170, 230, 288)-net over F₃, using

t-expansion [i] based on digital (169, 230, 288)-net over F₃, using
- 7 times m-reduction [i] based on digital (169, 237, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 79, 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]

(230−60, 230, 810)-Net over F₃ — Digital

Digital (170, 230, 810)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−60, 230, 27366)-Net in Base 3 — Upper bound on s

There is no (170, 230, 27367)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 712429 057816 732835 022268 148553 394482 319401 748022 131905 280518 202938 686888 376789 033332 922292 637490 255213 686869 > 3²³⁰ [i]