MinT - Best Known (141−51, 141, s)-Nets in Base 3

Best Known (141−51, 141, s)-Nets in Base 3

(141−51, 141, 148)-Net over F₃ — Constructive and digital

Digital (90, 141, 148)-net over F₃, using

5 times m-reduction [i] based on digital (90, 146, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 73, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(141−51, 141, 185)-Net over F₃ — Digital

Digital (90, 141, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−51, 141, 2366)-Net in Base 3 — Upper bound on s

There is no (90, 141, 2367)-net in base 3, because

1 times m-reduction [i] would yield (90, 140, 2367)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 329800 616566 492335 565549 048480 017092 106573 147322 719126 803814 820431 > 3¹⁴⁰ [i]