MinT - Best Known (174−73, 174, s)-Nets in Base 3

Best Known (174−73, 174, s)-Nets in Base 3

(174−73, 174, 128)-Net over F₃ — Constructive and digital

Digital (101, 174, 128)-net over F₃, using

2 times m-reduction [i] based on digital (101, 176, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 88, 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]

(174−73, 174, 145)-Net over F₃ — Digital

Digital (101, 174, 145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−73, 174, 1366)-Net in Base 3 — Upper bound on s

There is no (101, 174, 1367)-net in base 3, because

1 times m-reduction [i] would yield (101, 173, 1367)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35556 672614 350475 640280 214389 032136 625535 160181 648705 416060 243657 250842 107924 873785 > 3¹⁷³ [i]