MinT - Best Known (128, 223, s)-Nets in Base 3

Best Known (128, 223, s)-Nets in Base 3

(128, 223, 128)-Net over F₃ — Constructive and digital

Digital (128, 223, 128)-net over F₃, using

7 times m-reduction [i] based on digital (128, 230, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 115, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(128, 223, 172)-Net over F₃ — Digital

Digital (128, 223, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 223, 1601)-Net in Base 3 — Upper bound on s

There is no (128, 223, 1602)-net in base 3, because

1 times m-reduction [i] would yield (128, 222, 1602)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8555 529362 062935 645333 446675 822155 511733 363038 415636 774538 617508 993484 523806 081038 203674 012790 543223 823961 > 3²²² [i]