MinT - Best Known (222−94, 222, s)-Nets in Base 3

Best Known (222−94, 222, s)-Nets in Base 3

(222−94, 222, 148)-Net over F₃ — Constructive and digital

Digital (128, 222, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 111, 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]

(222−94, 222, 175)-Net over F₃ — Digital

Digital (128, 222, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−94, 222, 1601)-Net in Base 3 — Upper bound on s

There is no (128, 222, 1602)-net in base 3, because

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]