MinT - Best Known (206−55, 206, s)-Nets in Base 3

Best Known (206−55, 206, s)-Nets in Base 3

(206−55, 206, 288)-Net over F₃ — Constructive and digital

Digital (151, 206, 288)-net over F₃, using

4 times m-reduction [i] based on digital (151, 210, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 70, 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]

(206−55, 206, 678)-Net over F₃ — Digital

Digital (151, 206, 678)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−55, 206, 22880)-Net in Base 3 — Upper bound on s

There is no (151, 206, 22881)-net in base 3, because

1 times m-reduction [i] would yield (151, 205, 22881)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 597886 240352 812577 211670 291325 312979 863606 149471 114382 071837 676327 200051 514264 074841 430569 881147 > 3²⁰⁵ [i]