MinT - Best Known (239−98, 239, s)-Nets in Base 3

Best Known (239−98, 239, s)-Nets in Base 3

(239−98, 239, 148)-Net over F₃ — Constructive and digital

Digital (141, 239, 148)-net over F₃, using

9 times m-reduction [i] based on digital (141, 248, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 124, 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]

(239−98, 239, 204)-Net over F₃ — Digital

Digital (141, 239, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−98, 239, 1981)-Net in Base 3 — Upper bound on s

There is no (141, 239, 1982)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 081209 670725 415148 007362 466951 493265 766507 659284 875991 842617 650153 796033 661460 908365 412355 908030 825863 926724 604189 > 3²³⁹ [i]