MinT - Best Known (219−101, 219, s)-Nets in Base 3

Best Known (219−101, 219, s)-Nets in Base 3

(219−101, 219, 80)-Net over F₃ — Constructive and digital

Digital (118, 219, 80)-net over F₃, using

1 times m-reduction [i] based on digital (118, 220, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 110, 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]

(219−101, 219, 136)-Net over F₃ — Digital

Digital (118, 219, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−101, 219, 1123)-Net in Base 3 — Upper bound on s

There is no (118, 219, 1124)-net in base 3, because

1 times m-reduction [i] would yield (118, 218, 1124)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 368455 058819 208576 402920 614924 347930 120785 973516 395946 501759 702081 638523 961429 463564 644517 362493 248121 > 3²¹⁸ [i]