MinT - Best Known (150, 150+53, s)-Nets in Base 3

Best Known (150, 150+53, s)-Nets in Base 3

(150, 150+53, 288)-Net over F₃ — Constructive and digital

Digital (150, 203, 288)-net over F₃, using

t-expansion [i] based on digital (149, 203, 288)-net over F₃, using
- 4 times m-reduction [i] based on digital (149, 207, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 69, 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]

(150, 150+53, 727)-Net over F₃ — Digital

Digital (150, 203, 727)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+53, 26835)-Net in Base 3 — Upper bound on s

There is no (150, 203, 26836)-net in base 3, because

1 times m-reduction [i] would yield (150, 202, 26836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 390800 792050 600374 133040 881266 491280 962523 459805 836835 455527 943099 755966 104204 031694 713583 341977 > 3²⁰² [i]