MinT - Best Known (181−70, 181, s)-Nets in Base 3

Best Known (181−70, 181, s)-Nets in Base 3

(181−70, 181, 148)-Net over F₃ — Constructive and digital

Digital (111, 181, 148)-net over F₃, using

7 times m-reduction [i] based on digital (111, 188, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 94, 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]

(181−70, 181, 189)-Net over F₃ — Digital

Digital (111, 181, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−70, 181, 2005)-Net in Base 3 — Upper bound on s

There is no (111, 181, 2006)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 229 509046 153656 792791 165926 330692 284558 546292 063907 076539 870911 673473 408424 311752 189793 > 3¹⁸¹ [i]