MinT - Best Known (227−86, 227, s)-Nets in Base 3

Best Known (227−86, 227, s)-Nets in Base 3

(227−86, 227, 156)-Net over F₃ — Constructive and digital

Digital (141, 227, 156)-net over F₃, using

11 times m-reduction [i] based on digital (141, 238, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 119, 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]

(227−86, 227, 244)-Net over F₃ — Digital

Digital (141, 227, 244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−86, 227, 2745)-Net in Base 3 — Upper bound on s

There is no (141, 227, 2746)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 052508 858253 070709 637420 594455 052597 253366 157625 918939 905012 285031 540445 555082 478151 595974 654705 976128 331617 > 3²²⁷ [i]