MinT - Best Known (177, 177+50, s)-Nets in Base 3

Best Known (177, 177+50, s)-Nets in Base 3

(177, 177+50, 640)-Net over F₃ — Constructive and digital

Digital (177, 227, 640)-net over F₃, using

t-expansion [i] based on digital (176, 227, 640)-net over F₃, using
- 1 times m-reduction [i] based on digital (176, 228, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 57, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(177, 177+50, 1575)-Net over F₃ — Digital

Digital (177, 227, 1575)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+50, 109335)-Net in Base 3 — Upper bound on s

There is no (177, 227, 109336)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 025891 415989 841222 976689 058560 112739 094522 023172 597005 535689 312614 495559 197003 444834 372674 297868 818281 200049 > 3²²⁷ [i]