MinT - Best Known (205−83, 205, s)-Nets in Base 3

Best Known (205−83, 205, s)-Nets in Base 3

(205−83, 205, 148)-Net over F₃ — Constructive and digital

Digital (122, 205, 148)-net over F₃, using

5 times m-reduction [i] based on digital (122, 210, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 105, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(205−83, 205, 184)-Net over F₃ — Digital

Digital (122, 205, 184)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−83, 205, 1869)-Net in Base 3 — Upper bound on s

There is no (122, 205, 1870)-net in base 3, because

1 times m-reduction [i] would yield (122, 204, 1870)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 954675 705539 271181 474390 561034 966874 904311 146759 422249 763926 853355 857932 347331 284110 886017 600205 > 3²⁰⁴ [i]