MinT - Best Known (172−70, 172, s)-Nets in Base 3

Best Known (172−70, 172, s)-Nets in Base 3

(172−70, 172, 128)-Net over F₃ — Constructive and digital

Digital (102, 172, 128)-net over F₃, using

6 times m-reduction [i] based on digital (102, 178, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 89, 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]

(172−70, 172, 156)-Net over F₃ — Digital

Digital (102, 172, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−70, 172, 1503)-Net in Base 3 — Upper bound on s

There is no (102, 172, 1504)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11670 127600 787394 026728 737949 608442 113256 423682 428008 971119 529777 959488 140733 174657 > 3¹⁷² [i]