MinT - Best Known (124, 124+53, s)-Nets in Base 3

Best Known (124, 124+53, s)-Nets in Base 3

(124, 124+53, 228)-Net over F₃ — Constructive and digital

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, 124+53, 401)-Net over F₃ — Digital

Digital (124, 177, 401)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+53, 8928)-Net in Base 3 — Upper bound on s

There is no (124, 177, 8929)-net in base 3, because

1 times m-reduction [i] would yield (124, 176, 8929)-net in base 3, but
- 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]