MinT - Best Known (233−100, 233, s)-Nets in Base 3

Best Known (233−100, 233, s)-Nets in Base 3

(233−100, 233, 128)-Net over F₃ — Constructive and digital

Digital (133, 233, 128)-net over F₃, using

7 times m-reduction [i] based on digital (133, 240, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 120, 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]

(233−100, 233, 175)-Net over F₃ — Digital

Digital (133, 233, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−100, 233, 1580)-Net in Base 3 — Upper bound on s

There is no (133, 233, 1581)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1500 543732 040901 222129 558048 245519 707713 428278 963294 815752 700427 336653 335134 723230 015407 812181 571856 691401 903777 > 3²³³ [i]