MinT - Best Known (129−32, 129, s)-Nets in Base 2

Best Known (129−32, 129, s)-Nets in Base 2

(129−32, 129, 144)-Net over F₂ — Constructive and digital

Digital (97, 129, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 43, 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]

(129−32, 129, 200)-Net over F₂ — Digital

Digital (97, 129, 200)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−32, 129, 1794)-Net in Base 2 — Upper bound on s

There is no (97, 129, 1795)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 682 763732 304805 798642 519347 717896 936208 > 2¹²⁹ [i]