MinT - Best Known (205−49, 205, s)-Nets in Base 2

Best Known (205−49, 205, s)-Nets in Base 2

(205−49, 205, 195)-Net over F₂ — Constructive and digital

Digital (156, 205, 195)-net over F₂, using

8 times m-reduction [i] based on digital (156, 213, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 71, 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]

(205−49, 205, 322)-Net over F₂ — Digital

Digital (156, 205, 322)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−49, 205, 3513)-Net in Base 2 — Upper bound on s

There is no (156, 205, 3514)-net in base 2, because

1 times m-reduction [i] would yield (156, 204, 3514)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 753303 400058 959078 674675 814247 695250 640302 306090 895485 699323 > 2²⁰⁴ [i]