MinT - Best Known (147−55, 147, s)-Nets in Base 3

Best Known (147−55, 147, s)-Nets in Base 3

(147−55, 147, 148)-Net over F₃ — Constructive and digital

Digital (92, 147, 148)-net over F₃, using

3 times m-reduction [i] based on digital (92, 150, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 75, 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]

(147−55, 147, 174)-Net over F₃ — Digital

Digital (92, 147, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−55, 147, 2050)-Net in Base 3 — Upper bound on s

There is no (92, 147, 2051)-net in base 3, because

1 times m-reduction [i] would yield (92, 146, 2051)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4609 384469 128300 601228 956932 814383 967364 852383 979162 429963 214780 689403 > 3¹⁴⁶ [i]