MinT - Best Known (124, 176, s)-Nets in Base 3

Best Known (124, 176, s)-Nets in Base 3

(124, 176, 228)-Net over F₃ — Constructive and digital

Digital (124, 176, 228)-net over F₃, using

1 times m-reduction [i] based on digital (124, 177, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 59, 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]

(124, 176, 417)-Net over F₃ — Digital

Digital (124, 176, 417)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 176, 8928)-Net in Base 3 — Upper bound on s

There is no (124, 176, 8929)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 942318 018795 217669 954490 447438 818046 567161 656083 254265 018935 726733 273678 615318 864553 > 3¹⁷⁶ [i]