MinT - Best Known (126, 167, s)-Nets in Base 2

Best Known (126, 167, s)-Nets in Base 2

(126, 167, 195)-Net over F₂ — Constructive and digital

Digital (126, 167, 195)-net over F₂, using

1 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]

(126, 167, 253)-Net over F₂ — Digital

Digital (126, 167, 253)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 167, 2587)-Net in Base 2 — Upper bound on s

There is no (126, 167, 2588)-net in base 2, because

1 times m-reduction [i] would yield (126, 166, 2588)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 93 564175 415788 979309 159376 573964 248619 721900 145374 > 2¹⁶⁶ [i]