MinT - Best Known (168−37, 168, s)-Nets in Base 2

Best Known (168−37, 168, s)-Nets in Base 2

(168−37, 168, 196)-Net over F₂ — Constructive and digital

Digital (131, 168, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 42, 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]

(168−37, 168, 340)-Net over F₂ — Digital

Digital (131, 168, 340)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−37, 168, 4661)-Net in Base 2 — Upper bound on s

There is no (131, 168, 4662)-net in base 2, because

1 times m-reduction [i] would yield (131, 167, 4662)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 187 135553 618319 202962 199501 804933 860941 350124 680550 > 2¹⁶⁷ [i]