MinT - Best Known (136−43, 136, s)-Nets in Base 3

Best Known (136−43, 136, s)-Nets in Base 3

(136−43, 136, 156)-Net over F₃ — Constructive and digital

Digital (93, 136, 156)-net over F₃, using

6 times m-reduction [i] based on digital (93, 142, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 71, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(136−43, 136, 271)-Net over F₃ — Digital

Digital (93, 136, 271)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−43, 136, 5045)-Net in Base 3 — Upper bound on s

There is no (93, 136, 5046)-net in base 3, because

1 times m-reduction [i] would yield (93, 135, 5046)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25828 111365 379750 311766 423618 526321 383119 922685 196704 321002 965413 > 3¹³⁵ [i]