MinT - Best Known (108, 108+67, s)-Nets in Base 3

Best Known (108, 108+67, s)-Nets in Base 3

(108, 108+67, 148)-Net over F₃ — Constructive and digital

Digital (108, 175, 148)-net over F₃, using

7 times m-reduction [i] based on digital (108, 182, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 91, 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]

(108, 108+67, 189)-Net over F₃ — Digital

Digital (108, 175, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+67, 2125)-Net in Base 3 — Upper bound on s

There is no (108, 175, 2126)-net in base 3, because

1 times m-reduction [i] would yield (108, 174, 2126)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104948 360587 015842 157018 651280 570206 772354 831152 722772 790402 914086 570268 188248 678493 > 3¹⁷⁴ [i]