MinT - Best Known (105, 178, s)-Nets in Base 3

Best Known (105, 178, s)-Nets in Base 3

(105, 178, 128)-Net over F₃ — Constructive and digital

Digital (105, 178, 128)-net over F₃, using

6 times m-reduction [i] based on digital (105, 184, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 92, 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]

(105, 178, 157)-Net over F₃ — Digital

Digital (105, 178, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 178, 1548)-Net in Base 3 — Upper bound on s

There is no (105, 178, 1549)-net in base 3, because

1 times m-reduction [i] would yield (105, 177, 1549)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 880230 345984 911018 031159 652548 034795 526503 311966 409507 799551 410764 450747 082216 712465 > 3¹⁷⁷ [i]