MinT - Best Known (149−57, 149, s)-Nets in Base 3

Best Known (149−57, 149, s)-Nets in Base 3

(149−57, 149, 148)-Net over F₃ — Constructive and digital

Digital (92, 149, 148)-net over F₃, using

1 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]

(149−57, 149, 165)-Net over F₃ — Digital

Digital (92, 149, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−57, 149, 1851)-Net in Base 3 — Upper bound on s

There is no (92, 149, 1852)-net in base 3, because

1 times m-reduction [i] would yield (92, 148, 1852)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41381 364821 851154 884549 125469 571398 360261 016289 697432 331957 478967 567041 > 3¹⁴⁸ [i]