MinT - Best Known (248−104, 248, s)-Nets in Base 3

Best Known (248−104, 248, s)-Nets in Base 3

(248−104, 248, 148)-Net over F₃ — Constructive and digital

Digital (144, 248, 148)-net over F₃, using

t-expansion [i] based on digital (142, 248, 148)-net over F₃, using
- 2 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 125, 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]

(248−104, 248, 198)-Net over F₃ — Digital

Digital (144, 248, 198)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−104, 248, 1856)-Net in Base 3 — Upper bound on s

There is no (144, 248, 1857)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21684 102341 781162 639766 418462 328378 295162 205440 833394 122781 597345 768409 029507 866225 636074 623614 544000 388402 527977 094161 > 3²⁴⁸ [i]