MinT - Best Known (140−49, 140, s)-Nets in Base 3

Best Known (140−49, 140, s)-Nets in Base 3

(140−49, 140, 148)-Net over F₃ — Constructive and digital

Digital (91, 140, 148)-net over F₃, using

8 times m-reduction [i] based on digital (91, 148, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 74, 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]

(140−49, 140, 204)-Net over F₃ — Digital

Digital (91, 140, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−49, 140, 2818)-Net in Base 3 — Upper bound on s

There is no (91, 140, 2819)-net in base 3, because

1 times m-reduction [i] would yield (91, 139, 2819)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 091842 591137 082349 559251 791876 905471 087320 229358 919500 889587 445969 > 3¹³⁹ [i]