MinT - Best Known (117−48, 117, s)-Nets in Base 3

Best Known (117−48, 117, s)-Nets in Base 3

(117−48, 117, 80)-Net over F₃ — Constructive and digital

Digital (69, 117, 80)-net over F₃, using

5 times m-reduction [i] based on digital (69, 122, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 61, 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]

(117−48, 117, 111)-Net over F₃ — Digital

Digital (69, 117, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−48, 117, 1014)-Net in Base 3 — Upper bound on s

There is no (69, 117, 1015)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66 613936 529260 501250 617603 459833 171908 716287 223417 644369 > 3¹¹⁷ [i]