MinT - Best Known (145−51, 145, s)-Nets in Base 3

Best Known (145−51, 145, s)-Nets in Base 3

(145−51, 145, 148)-Net over F₃ — Constructive and digital

Digital (94, 145, 148)-net over F₃, using

9 times m-reduction [i] based on digital (94, 154, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 77, 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]

(145−51, 145, 206)-Net over F₃ — Digital

Digital (94, 145, 206)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−51, 145, 2825)-Net in Base 3 — Upper bound on s

There is no (94, 145, 2826)-net in base 3, because

1 times m-reduction [i] would yield (94, 144, 2826)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 510 265893 163618 016480 361814 050876 922143 411727 494423 994535 217655 033509 > 3¹⁴⁴ [i]