MinT - Best Known (233−101, 233, s)-Nets in Base 3

Best Known (233−101, 233, s)-Nets in Base 3

(233−101, 233, 128)-Net over F₃ — Constructive and digital

Digital (132, 233, 128)-net over F₃, using

5 times m-reduction [i] based on digital (132, 238, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 119, 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]

(233−101, 233, 170)-Net over F₃ — Digital

Digital (132, 233, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−101, 233, 1545)-Net in Base 3 — Upper bound on s

There is no (132, 233, 1546)-net in base 3, because

1 times m-reduction [i] would yield (132, 232, 1546)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 506 625984 611985 978902 411641 025798 410909 048926 403693 639158 261773 273040 202508 243718 192538 943700 090601 903928 679141 > 3²³² [i]