MinT - Best Known (176, 176+51, s)-Nets in Base 3

Best Known (176, 176+51, s)-Nets in Base 3

(176, 176+51, 640)-Net over F₃ — Constructive and digital

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]

(176, 176+51, 1453)-Net over F₃ — Digital

Digital (176, 227, 1453)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+51, 104633)-Net in Base 3 — Upper bound on s

There is no (176, 227, 104634)-net in base 3, because

1 times m-reduction [i] would yield (176, 226, 104634)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675253 142401 417715 581801 370771 175141 064515 755520 857920 816457 139469 494386 188322 837476 293076 873134 968936 685573 > 3²²⁶ [i]