MinT - Best Known (172−71, 172, s)-Nets in Base 3

Best Known (172−71, 172, s)-Nets in Base 3

(172−71, 172, 128)-Net over F₃ — Constructive and digital

Digital (101, 172, 128)-net over F₃, using

4 times m-reduction [i] based on digital (101, 176, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 88, 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]

(172−71, 172, 150)-Net over F₃ — Digital

Digital (101, 172, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−71, 172, 1456)-Net in Base 3 — Upper bound on s

There is no (101, 172, 1457)-net in base 3, because

1 times m-reduction [i] would yield (101, 171, 1457)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3938 006576 991761 401205 254306 111069 192108 457238 414019 715264 496842 772228 387846 428379 > 3¹⁷¹ [i]