MinT - Best Known (207−83, 207, s)-Nets in Base 3

Best Known (207−83, 207, s)-Nets in Base 3

(207−83, 207, 148)-Net over F₃ — Constructive and digital

Digital (124, 207, 148)-net over F₃, using

7 times m-reduction [i] based on digital (124, 214, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 107, 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]

(207−83, 207, 191)-Net over F₃ — Digital

Digital (124, 207, 191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−83, 207, 1974)-Net in Base 3 — Upper bound on s

There is no (124, 207, 1975)-net in base 3, because

1 times m-reduction [i] would yield (124, 206, 1975)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 197 027385 137560 960599 937644 751561 643269 156810 029107 004059 763921 262141 014738 874349 281248 387854 574879 > 3²⁰⁶ [i]