MinT - Best Known (166−39, 166, s)-Nets in Base 3

Best Known (166−39, 166, s)-Nets in Base 3

(166−39, 166, 464)-Net over F₃ — Constructive and digital

Digital (127, 166, 464)-net over F₃, using

3² times duplication [i] based on digital (125, 164, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 41, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(166−39, 166, 931)-Net over F₃ — Digital

Digital (127, 166, 931)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−39, 166, 55139)-Net in Base 3 — Upper bound on s

There is no (127, 166, 55140)-net in base 3, because

1 times m-reduction [i] would yield (127, 165, 55140)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 310206 460453 351714 448755 330021 859589 857509 986572 566407 154422 611429 432863 364401 > 3¹⁶⁵ [i]