MinT - Best Known (206−53, 206, s)-Nets in Base 3

Best Known (206−53, 206, s)-Nets in Base 3

(206−53, 206, 288)-Net over F₃ — Constructive and digital

Digital (153, 206, 288)-net over F₃, using

7 times m-reduction [i] based on digital (153, 213, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 71, 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]

(206−53, 206, 778)-Net over F₃ — Digital

Digital (153, 206, 778)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−53, 206, 30466)-Net in Base 3 — Upper bound on s

There is no (153, 206, 30467)-net in base 3, because

1 times m-reduction [i] would yield (153, 205, 30467)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 591653 900060 873467 651017 302472 753660 909606 445356 694737 369105 140425 480264 626614 321865 124396 394165 > 3²⁰⁵ [i]