MinT - Best Known (127−47, 127, s)-Nets in Base 3

Best Known (127−47, 127, s)-Nets in Base 3

(127−47, 127, 128)-Net over F₃ — Constructive and digital

Digital (80, 127, 128)-net over F₃, using

7 times m-reduction [i] based on digital (80, 134, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 67, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(127−47, 127, 159)-Net over F₃ — Digital

Digital (80, 127, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−47, 127, 1915)-Net in Base 3 — Upper bound on s

There is no (80, 127, 1916)-net in base 3, because

1 times m-reduction [i] would yield (80, 126, 1916)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 325408 301347 223216 294439 043822 072200 135858 569310 942031 736081 > 3¹²⁶ [i]