MinT - Best Known (234−91, 234, s)-Nets in Base 3

Best Known (234−91, 234, s)-Nets in Base 3

(234−91, 234, 156)-Net over F₃ — Constructive and digital

Digital (143, 234, 156)-net over F₃, using

8 times m-reduction [i] based on digital (143, 242, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 121, 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]

(234−91, 234, 232)-Net over F₃ — Digital

Digital (143, 234, 232)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−91, 234, 2559)-Net in Base 3 — Upper bound on s

There is no (143, 234, 2560)-net in base 3, because

1 times m-reduction [i] would yield (143, 233, 2560)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1492 020600 319870 440599 132623 727764 350456 552497 616832 221100 401271 445853 639005 460736 535384 950160 852668 234883 396609 > 3²³³ [i]