MinT - Best Known (172−76, 172, s)-Nets in Base 3

Best Known (172−76, 172, s)-Nets in Base 3

(172−76, 172, 80)-Net over F₃ — Constructive and digital

Digital (96, 172, 80)-net over F₃, using

4 times m-reduction [i] based on digital (96, 176, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 88, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(172−76, 172, 124)-Net over F₃ — Digital

Digital (96, 172, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−76, 172, 1047)-Net in Base 3 — Upper bound on s

There is no (96, 172, 1048)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11654 086831 142847 356775 315513 171723 756586 014574 160170 524299 986362 151031 614328 422545 > 3¹⁷² [i]