MinT - Best Known (172−72, 172, s)-Nets in Base 3

Best Known (172−72, 172, s)-Nets in Base 3

(172−72, 172, 128)-Net over F₃ — Constructive and digital

Digital (100, 172, 128)-net over F₃, using

2 times m-reduction [i] based on digital (100, 174, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 87, 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]

(172−72, 172, 144)-Net over F₃ — Digital

Digital (100, 172, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−72, 172, 1324)-Net in Base 3 — Upper bound on s

There is no (100, 172, 1325)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11893 468020 827012 914746 146167 771390 691369 211128 351165 621648 107281 974389 177478 978577 > 3¹⁷² [i]