MinT - Best Known (156−62, 156, s)-Nets in Base 3

Best Known (156−62, 156, s)-Nets in Base 3

(156−62, 156, 128)-Net over F₃ — Constructive and digital

Digital (94, 156, 128)-net over F₃, using

6 times m-reduction [i] based on digital (94, 162, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 81, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(156−62, 156, 154)-Net over F₃ — Digital

Digital (94, 156, 154)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−62, 156, 1532)-Net in Base 3 — Upper bound on s

There is no (94, 156, 1533)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270 286493 444247 719461 357678 176603 248400 860149 699047 812508 531134 959610 306715 > 3¹⁵⁶ [i]