MinT - Best Known (158, 158+44, s)-Nets in Base 3

Best Known (158, 158+44, s)-Nets in Base 3

(158, 158+44, 640)-Net over F₃ — Constructive and digital

Digital (158, 202, 640)-net over F₃, using

2 times m-reduction [i] based on digital (158, 204, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 51, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(158, 158+44, 1493)-Net over F₃ — Digital

Digital (158, 202, 1493)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+44, 108787)-Net in Base 3 — Upper bound on s

There is no (158, 202, 108788)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 390909 172898 579509 997784 293175 293877 140975 503303 921985 281419 909226 815975 404158 703030 472600 590713 > 3²⁰² [i]