MinT - Best Known (127, 127+39, s)-Nets in Base 2

Best Known (127, 127+39, s)-Nets in Base 2

(127, 127+39, 195)-Net over F₂ — Constructive and digital

Digital (127, 166, 195)-net over F₂, using

t-expansion [i] based on digital (126, 166, 195)-net over F₂, using
- 2 times m-reduction [i] based on digital (126, 168, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 56, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(127, 127+39, 282)-Net over F₂ — Digital

Digital (127, 166, 282)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+39, 3233)-Net in Base 2 — Upper bound on s

There is no (127, 166, 3234)-net in base 2, because

1 times m-reduction [i] would yield (127, 165, 3234)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 862458 329831 085581 844647 655782 770257 318026 625000 > 2¹⁶⁵ [i]