MinT - Best Known (140, 229, s)-Nets in Base 3

Best Known (140, 229, s)-Nets in Base 3

(140, 229, 156)-Net over F₃ — Constructive and digital

Digital (140, 229, 156)-net over F₃, using

7 times m-reduction [i] based on digital (140, 236, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 118, 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]

(140, 229, 228)-Net over F₃ — Digital

Digital (140, 229, 228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 229, 2516)-Net in Base 3 — Upper bound on s

There is no (140, 229, 2517)-net in base 3, because

1 times m-reduction [i] would yield (140, 228, 2517)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 091576 198396 651505 387197 439399 792795 242059 692457 765449 476366 476750 673189 850876 513376 802684 782994 015568 807985 > 3²²⁸ [i]