MinT - Best Known (179−78, 179, s)-Nets in Base 3

Best Known (179−78, 179, s)-Nets in Base 3

(179−78, 179, 80)-Net over F₃ — Constructive and digital

Digital (101, 179, 80)-net over F₃, using

7 times m-reduction [i] based on digital (101, 186, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 93, 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]

(179−78, 179, 134)-Net over F₃ — Digital

Digital (101, 179, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−78, 179, 1153)-Net in Base 3 — Upper bound on s

There is no (101, 179, 1154)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 422390 156487 056721 069891 624896 001850 702627 610249 499476 674982 454129 476412 855534 130985 > 3¹⁷⁹ [i]