MinT - Best Known (206−79, 206, s)-Nets in Base 3

Best Known (206−79, 206, s)-Nets in Base 3

(206−79, 206, 156)-Net over F₃ — Constructive and digital

Digital (127, 206, 156)-net over F₃, using

4 times m-reduction [i] based on digital (127, 210, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 105, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(206−79, 206, 216)-Net over F₃ — Digital

Digital (127, 206, 216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−79, 206, 2441)-Net in Base 3 — Upper bound on s

There is no (127, 206, 2442)-net in base 3, because

1 times m-reduction [i] would yield (127, 205, 2442)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65 452360 689702 270973 505106 875608 969160 333502 727865 738306 534820 423858 131413 705187 748394 267391 015433 > 3²⁰⁵ [i]