MinT - Best Known (189−55, 189, s)-Nets in Base 3

Best Known (189−55, 189, s)-Nets in Base 3

(189−55, 189, 252)-Net over F₃ — Constructive and digital

Digital (134, 189, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 63, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(189−55, 189, 466)-Net over F₃ — Digital

Digital (134, 189, 466)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−55, 189, 11443)-Net in Base 3 — Upper bound on s

There is no (134, 189, 11444)-net in base 3, because

1 times m-reduction [i] would yield (134, 188, 11444)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 500638 668615 282984 205549 263046 170730 652485 689545 881621 012546 017964 874772 966501 612551 724849 > 3¹⁸⁸ [i]