MinT - Best Known (128−27, 128, s)-Nets in Base 2

Best Known (128−27, 128, s)-Nets in Base 2

(128−27, 128, 196)-Net over F₂ — Constructive and digital

Digital (101, 128, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 32, 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]

(128−27, 128, 314)-Net over F₂ — Digital

Digital (101, 128, 314)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−27, 128, 4926)-Net in Base 2 — Upper bound on s

There is no (101, 128, 4927)-net in base 2, because

1 times m-reduction [i] would yield (101, 127, 4927)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 170 210207 195334 084670 131870 648425 307540 > 2¹²⁷ [i]