MinT - Best Known (224−93, 224, s)-Nets in Base 3

Best Known (224−93, 224, s)-Nets in Base 3

(224−93, 224, 148)-Net over F₃ — Constructive and digital

Digital (131, 224, 148)-net over F₃, using

4 times m-reduction [i] based on digital (131, 228, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 114, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(224−93, 224, 186)-Net over F₃ — Digital

Digital (131, 224, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−93, 224, 1805)-Net in Base 3 — Upper bound on s

There is no (131, 224, 1806)-net in base 3, because

1 times m-reduction [i] would yield (131, 223, 1806)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25581 847570 062661 775069 661626 694347 318118 089486 311022 695541 214495 599437 050440 361522 944000 353385 999988 870357 > 3²²³ [i]