MinT - Best Known (159−47, 159, s)-Nets in Base 3

Best Known (159−47, 159, s)-Nets in Base 3

(159−47, 159, 228)-Net over F₃ — Constructive and digital

Digital (112, 159, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 53, 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]

(159−47, 159, 383)-Net over F₃ — Digital

Digital (112, 159, 383)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−47, 159, 8911)-Net in Base 3 — Upper bound on s

There is no (112, 159, 8912)-net in base 3, because

1 times m-reduction [i] would yield (112, 158, 8912)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2430 999305 742117 167205 156278 060620 474103 386594 064905 197809 956617 880190 280129 > 3¹⁵⁸ [i]