MinT - Best Known (156, 156+52, s)-Nets in Base 3

Best Known (156, 156+52, s)-Nets in Base 3

(156, 156+52, 328)-Net over F₃ — Constructive and digital

Digital (156, 208, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 52, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(156, 156+52, 877)-Net over F₃ — Digital

Digital (156, 208, 877)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+52, 34587)-Net in Base 3 — Upper bound on s

There is no (156, 208, 34588)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1743 980853 468498 800707 044460 594347 433156 398660 748680 561383 594483 704253 299751 239134 699278 541483 309513 > 3²⁰⁸ [i]