MinT - Best Known (144−31, 144, s)-Nets in Base 2

Best Known (144−31, 144, s)-Nets in Base 2

(144−31, 144, 196)-Net over F₂ — Constructive and digital

Digital (113, 144, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 36, 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]

(144−31, 144, 322)-Net over F₂ — Digital

Digital (113, 144, 322)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−31, 144, 4737)-Net in Base 2 — Upper bound on s

There is no (113, 144, 4738)-net in base 2, because

1 times m-reduction [i] would yield (113, 143, 4738)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 156854 803838 363704 832564 167986 743890 387648 > 2¹⁴³ [i]