MinT - Best Known (235−97, 235, s)-Nets in Base 3

Best Known (235−97, 235, s)-Nets in Base 3

(235−97, 235, 148)-Net over F₃ — Constructive and digital

Digital (138, 235, 148)-net over F₃, using

7 times m-reduction [i] based on digital (138, 242, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 121, 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]

(235−97, 235, 197)-Net over F₃ — Digital

Digital (138, 235, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−97, 235, 1937)-Net in Base 3 — Upper bound on s

There is no (138, 235, 1938)-net in base 3, because

1 times m-reduction [i] would yield (138, 234, 1938)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4450 108055 084780 386073 210200 455204 440047 759375 447478 566201 684884 454525 182393 251154 474845 923601 660877 724231 865313 > 3²³⁴ [i]