MinT - Best Known (120−39, 120, s)-Nets in Base 3

Best Known (120−39, 120, s)-Nets in Base 3

(120−39, 120, 148)-Net over F₃ — Constructive and digital

Digital (81, 120, 148)-net over F₃, using

8 times m-reduction [i] based on digital (81, 128, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 64, 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]

(120−39, 120, 225)-Net over F₃ — Digital

Digital (81, 120, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−39, 120, 3840)-Net in Base 3 — Upper bound on s

There is no (81, 120, 3841)-net in base 3, because

1 times m-reduction [i] would yield (81, 119, 3841)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 600 462664 017979 590195 223716 691328 184898 435925 275975 186395 > 3¹¹⁹ [i]