MinT - Best Known (70, 70+25, s)-Nets in Base 3

Best Known (70, 70+25, s)-Nets in Base 3

(70, 70+25, 228)-Net over F₃ — Constructive and digital

Digital (70, 95, 228)-net over F₃, using

1 times m-reduction [i] based on digital (70, 96, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 32, 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]

(70, 70+25, 391)-Net over F₃ — Digital

Digital (70, 95, 391)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+25, 14435)-Net in Base 3 — Upper bound on s

There is no (70, 95, 14436)-net in base 3, because

1 times m-reduction [i] would yield (70, 94, 14436)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707 186623 631413 514559 472344 243890 002054 819073 > 3⁹⁴ [i]