MinT - Best Known (221−89, 221, s)-Nets in Base 3

Best Known (221−89, 221, s)-Nets in Base 3

(221−89, 221, 148)-Net over F₃ — Constructive and digital

Digital (132, 221, 148)-net over F₃, using

9 times m-reduction [i] based on digital (132, 230, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 115, 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]

(221−89, 221, 200)-Net over F₃ — Digital

Digital (132, 221, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−89, 221, 2053)-Net in Base 3 — Upper bound on s

There is no (132, 221, 2054)-net in base 3, because

1 times m-reduction [i] would yield (132, 220, 2054)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 938 025581 346433 822055 207892 866820 610791 670188 411571 891812 344836 632802 194684 464247 769608 490121 758834 047897 > 3²²⁰ [i]