MinT - Best Known (205−73, 205, s)-Nets in Base 3

Best Known (205−73, 205, s)-Nets in Base 3

(205−73, 205, 156)-Net over F₃ — Constructive and digital

Digital (132, 205, 156)-net over F₃, using

15 times m-reduction [i] based on digital (132, 220, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 110, 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]

(205−73, 205, 266)-Net over F₃ — Digital

Digital (132, 205, 266)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−73, 205, 3573)-Net in Base 3 — Upper bound on s

There is no (132, 205, 3574)-net in base 3, because

1 times m-reduction [i] would yield (132, 204, 3574)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 577944 835212 844612 671286 454283 726261 875518 234809 918942 078210 862811 579354 865413 726007 563360 871753 > 3²⁰⁴ [i]