MinT - Best Known (129, 129+48, s)-Nets in Base 2

Best Known (129, 129+48, s)-Nets in Base 2

(129, 129+48, 144)-Net over F₂ — Constructive and digital

Digital (129, 177, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 59, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(129, 129+48, 205)-Net over F₂ — Digital

Digital (129, 177, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 129+48, 1592)-Net in Base 2 — Upper bound on s

There is no (129, 177, 1593)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 194072 927933 575058 884722 496213 589152 547416 512281 392603 > 2¹⁷⁷ [i]