MinT - Best Known (205−55, 205, s)-Nets in Base 3

Best Known (205−55, 205, s)-Nets in Base 3

(205−55, 205, 288)-Net over F₃ — Constructive and digital

Digital (150, 205, 288)-net over F₃, using

t-expansion [i] based on digital (149, 205, 288)-net over F₃, using
- 2 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]

(205−55, 205, 663)-Net over F₃ — Digital

Digital (150, 205, 663)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−55, 205, 21966)-Net in Base 3 — Upper bound on s

There is no (150, 205, 21967)-net in base 3, because

1 times m-reduction [i] would yield (150, 204, 21967)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 516288 787272 647121 856799 887667 456212 223950 303121 025261 622529 135083 966782 241390 030573 109902 183179 > 3²⁰⁴ [i]