MinT - Best Known (165−47, 165, s)-Nets in Base 3

Best Known (165−47, 165, s)-Nets in Base 3

(165−47, 165, 252)-Net over F₃ — Constructive and digital

Digital (118, 165, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 55, 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]

(165−47, 165, 447)-Net over F₃ — Digital

Digital (118, 165, 447)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−47, 165, 11876)-Net in Base 3 — Upper bound on s

There is no (118, 165, 11877)-net in base 3, because

1 times m-reduction [i] would yield (118, 164, 11877)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 771499 184980 691568 856798 510142 088279 868734 015875 689698 910409 614926 723087 240091 > 3¹⁶⁴ [i]