MinT - Best Known (147−43, 147, s)-Nets in Base 3

Best Known (147−43, 147, s)-Nets in Base 3

(147−43, 147, 228)-Net over F₃ — Constructive and digital

Digital (104, 147, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 49, 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]

(147−43, 147, 372)-Net over F₃ — Digital

Digital (104, 147, 372)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−43, 147, 8986)-Net in Base 3 — Upper bound on s

There is no (104, 147, 8987)-net in base 3, because

1 times m-reduction [i] would yield (104, 146, 8987)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4570 418235 247889 977234 146397 102376 778287 958454 684438 302357 910899 882575 > 3¹⁴⁶ [i]