MinT - Best Known (172−65, 172, s)-Nets in Base 3

Best Known (172−65, 172, s)-Nets in Base 3

(172−65, 172, 148)-Net over F₃ — Constructive and digital

Digital (107, 172, 148)-net over F₃, using

8 times m-reduction [i] based on digital (107, 180, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 90, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(172−65, 172, 193)-Net over F₃ — Digital

Digital (107, 172, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−65, 172, 2235)-Net in Base 3 — Upper bound on s

There is no (107, 172, 2236)-net in base 3, because

1 times m-reduction [i] would yield (107, 171, 2236)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3883 197509 804739 373168 005126 663118 002605 154161 691660 041746 968436 410236 448086 542593 > 3¹⁷¹ [i]