MinT - Best Known (139, 139+50, s)-Nets in Base 2

Best Known (139, 139+50, s)-Nets in Base 2

(139, 139+50, 144)-Net over F₂ — Constructive and digital

Digital (139, 189, 144)-net over F₂, using

3 times m-reduction [i] based on digital (139, 192, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 64, 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, 139+50, 231)-Net over F₂ — Digital

Digital (139, 189, 231)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+50, 1883)-Net in Base 2 — Upper bound on s

There is no (139, 189, 1884)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 786 532950 775139 072647 886761 324374 151109 779655 830785 973837 > 2¹⁸⁹ [i]