MinT - Best Known (117, 117+87, s)-Nets in Base 3

Best Known (117, 117+87, s)-Nets in Base 3

(117, 117+87, 128)-Net over F₃ — Constructive and digital

Digital (117, 204, 128)-net over F₃, using

4 times m-reduction [i] based on digital (117, 208, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 104, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(117, 117+87, 159)-Net over F₃ — Digital

Digital (117, 204, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+87, 1467)-Net in Base 3 — Upper bound on s

There is no (117, 204, 1468)-net in base 3, because

1 times m-reduction [i] would yield (117, 203, 1468)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 231955 637660 494394 603276 022956 597882 251810 109711 165587 555299 168969 331258 933820 726498 011495 551185 > 3²⁰³ [i]