MinT - Best Known (127, 164, s)-Nets in Base 3

Best Known (127, 164, s)-Nets in Base 3

(127, 164, 600)-Net over F₃ — Constructive and digital

Digital (127, 164, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 41, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(127, 164, 1082)-Net over F₃ — Digital

Digital (127, 164, 1082)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 164, 78995)-Net in Base 3 — Upper bound on s

There is no (127, 164, 78996)-net in base 3, because

1 times m-reduction [i] would yield (127, 163, 78996)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 589959 417452 056171 062465 747800 724969 463437 710513 765221 605714 380391 101771 329177 > 3¹⁶³ [i]