MinT - Best Known (244−101, 244, s)-Nets in Base 3

Best Known (244−101, 244, s)-Nets in Base 3

(244−101, 244, 148)-Net over F₃ — Constructive and digital

Digital (143, 244, 148)-net over F₃, using

t-expansion [i] based on digital (142, 244, 148)-net over F₃, using
- 6 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 125, 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]

(244−101, 244, 202)-Net over F₃ — Digital

Digital (143, 244, 202)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−101, 244, 1980)-Net in Base 3 — Upper bound on s

There is no (143, 244, 1981)-net in base 3, because

1 times m-reduction [i] would yield (143, 243, 1981)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 752567 727748 032002 343502 115575 189769 923683 403685 784202 998197 304276 442548 403163 954761 704937 088315 548906 468728 929601 > 3²⁴³ [i]