MinT - Best Known (107, 107+34, s)-Nets in Base 2

Best Known (107, 107+34, s)-Nets in Base 2

(107, 107+34, 144)-Net over F₂ — Constructive and digital

Digital (107, 141, 144)-net over F₂, using

3 times m-reduction [i] based on digital (107, 144, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 48, 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]

(107, 107+34, 231)-Net over F₂ — Digital

Digital (107, 141, 231)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+34, 2227)-Net in Base 2 — Upper bound on s

There is no (107, 141, 2228)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 789081 732879 954674 184269 187683 114735 300779 > 2¹⁴¹ [i]