MinT - Best Known (165−49, 165, s)-Nets in Base 3

Best Known (165−49, 165, s)-Nets in Base 3

(165−49, 165, 228)-Net over F₃ — Constructive and digital

Digital (116, 165, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 55, 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]

(165−49, 165, 389)-Net over F₃ — Digital

Digital (116, 165, 389)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−49, 165, 8902)-Net in Base 3 — Upper bound on s

There is no (116, 165, 8903)-net in base 3, because

1 times m-reduction [i] would yield (116, 164, 8903)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 771467 065917 585497 121962 118505 301821 255237 688266 009768 733478 554247 403244 853329 > 3¹⁶⁴ [i]