MinT - Best Known (139−34, 139, s)-Nets in Base 2

Best Known (139−34, 139, s)-Nets in Base 2

(139−34, 139, 144)-Net over F₂ — Constructive and digital

Digital (105, 139, 144)-net over F₂, using

2 times m-reduction [i] based on digital (105, 141, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 47, 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]

(139−34, 139, 220)-Net over F₂ — Digital

Digital (105, 139, 220)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−34, 139, 2051)-Net in Base 2 — Upper bound on s

There is no (105, 139, 2052)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 699631 178684 295678 068543 174550 804882 504064 > 2¹³⁹ [i]