MinT - Best Known (105, 164, s)-Nets in Base 3

Best Known (105, 164, s)-Nets in Base 3

(105, 164, 156)-Net over F₃ — Constructive and digital

Digital (105, 164, 156)-net over F₃, using

2 times m-reduction [i] based on digital (105, 166, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 83, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(105, 164, 214)-Net over F₃ — Digital

Digital (105, 164, 214)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 164, 2776)-Net in Base 3 — Upper bound on s

There is no (105, 164, 2777)-net in base 3, because

1 times m-reduction [i] would yield (105, 163, 2777)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 595783 924803 989471 995554 564964 701453 896390 248738 243415 550038 869197 743864 277315 > 3¹⁶³ [i]