MinT - Best Known (104−42, 104, s)-Nets in Base 3

Best Known (104−42, 104, s)-Nets in Base 3

(104−42, 104, 80)-Net over F₃ — Constructive and digital

Digital (62, 104, 80)-net over F₃, using

4 times m-reduction [i] based on digital (62, 108, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 54, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(104−42, 104, 108)-Net over F₃ — Digital

Digital (62, 104, 108)-net over F₃, using

trace code for nets [i] based on digital (10, 52, 54)-net over F₉, using
- net from sequence [i] based on digital (10, 53)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
    - a curve from the manYPoints database [i]

(104−42, 104, 980)-Net in Base 3 — Upper bound on s

There is no (62, 104, 981)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42 206034 987910 003877 868162 966018 556389 130384 393851 > 3¹⁰⁴ [i]