MinT - Best Known (224−95, 224, s)-Nets in Base 3

Best Known (224−95, 224, s)-Nets in Base 3

(224−95, 224, 148)-Net over F₃ — Constructive and digital

Digital (129, 224, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 112, 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]

(224−95, 224, 175)-Net over F₃ — Digital

Digital (129, 224, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−95, 224, 1640)-Net in Base 3 — Upper bound on s

There is no (129, 224, 1641)-net in base 3, because

1 times m-reduction [i] would yield (129, 223, 1641)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25693 705252 489619 214396 155615 731028 358781 618873 831464 458695 448996 755667 916704 990277 120298 178769 498078 110091 > 3²²³ [i]