MinT - Best Known (106, 139, s)-Nets in Base 2

Best Known (106, 139, s)-Nets in Base 2

(106, 139, 144)-Net over F₂ — Constructive and digital

Digital (106, 139, 144)-net over F₂, using

t-expansion [i] based on 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]

(106, 139, 238)-Net over F₂ — Digital

Digital (106, 139, 238)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 139, 2661)-Net in Base 2 — Upper bound on s

There is no (106, 139, 2662)-net in base 2, because

1 times m-reduction [i] would yield (106, 138, 2662)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 349576 812744 592753 358358 537305 033183 943354 > 2¹³⁸ [i]