MinT - Best Known (104−31, 104, s)-Nets in Base 3

Best Known (104−31, 104, s)-Nets in Base 3

(104−31, 104, 156)-Net over F₃ — Constructive and digital

Digital (73, 104, 156)-net over F₃, using

1 times m-reduction [i] based on digital (73, 105, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 35, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(104−31, 104, 266)-Net over F₃ — Digital

Digital (73, 104, 266)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−31, 104, 6052)-Net in Base 3 — Upper bound on s

There is no (73, 104, 6053)-net in base 3, because

1 times m-reduction [i] would yield (73, 103, 6053)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 934183 714248 615313 177062 018984 510629 698959 576827 > 3¹⁰³ [i]