MinT - Best Known (184−41, 184, s)-Nets in Base 3

Best Known (184−41, 184, s)-Nets in Base 3

(184−41, 184, 640)-Net over F₃ — Constructive and digital

Digital (143, 184, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 46, 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]

(184−41, 184, 1254)-Net over F₃ — Digital

Digital (143, 184, 1254)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−41, 184, 96349)-Net in Base 3 — Upper bound on s

There is no (143, 184, 96350)-net in base 3, because

1 times m-reduction [i] would yield (143, 183, 96350)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2057 156166 282517 248324 936671 894557 161407 468388 060123 905450 218286 842465 091028 267110 101161 > 3¹⁸³ [i]