MinT - Best Known (184−41, 184, s)-Nets in Base 2

Best Known (184−41, 184, s)-Nets in Base 2

(184−41, 184, 196)-Net over F₂ — Constructive and digital

Digital (143, 184, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 46, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(184−41, 184, 354)-Net over F₂ — Digital

Digital (143, 184, 354)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−41, 184, 4688)-Net in Base 2 — Upper bound on s

There is no (143, 184, 4689)-net in base 2, because

1 times m-reduction [i] would yield (143, 183, 4689)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 297034 587956 302867 899809 160426 098046 188329 898435 143424 > 2¹⁸³ [i]