MinT - Best Known (124, 124+120, s)-Nets in Base 3

Best Known (124, 124+120, s)-Nets in Base 3

(124, 124+120, 78)-Net over F₃ — Constructive and digital

Digital (124, 244, 78)-net over F₃, using

t-expansion [i] based on digital (121, 244, 78)-net over F₃, using
- net from sequence [i] based on digital (121, 77)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(124, 124+120, 125)-Net over F₃ — Digital

Digital (124, 244, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+120, 952)-Net in Base 3 — Upper bound on s

There is no (124, 244, 953)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 268 482257 240929 676722 617948 599619 458923 785650 151778 085902 497544 650135 146417 673621 027298 170482 590513 683403 558527 847153 > 3²⁴⁴ [i]