MinT - Best Known (172−38, 172, s)-Nets in Base 2

Best Known (172−38, 172, s)-Nets in Base 2

(172−38, 172, 196)-Net over F₂ — Constructive and digital

Digital (134, 172, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 43, 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]

(172−38, 172, 343)-Net over F₂ — Digital

Digital (134, 172, 343)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−38, 172, 4182)-Net in Base 2 — Upper bound on s

There is no (134, 172, 4183)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5998 732195 464211 553276 160291 164582 127863 236817 679470 > 2¹⁷² [i]