MinT - Best Known (167−49, 167, s)-Nets in Base 3

Best Known (167−49, 167, s)-Nets in Base 3

(167−49, 167, 228)-Net over F₃ — Constructive and digital

Digital (118, 167, 228)-net over F₃, using

1 times m-reduction [i] based on digital (118, 168, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 56, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(167−49, 167, 409)-Net over F₃ — Digital

Digital (118, 167, 409)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−49, 167, 9758)-Net in Base 3 — Upper bound on s

There is no (118, 167, 9759)-net in base 3, because

1 times m-reduction [i] would yield (118, 166, 9759)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15 950917 244203 396263 110756 480840 248028 738175 798343 541923 451316 462478 851084 144081 > 3¹⁶⁶ [i]