MinT - Best Known (240−57, 240, s)-Nets in Base 2

Best Known (240−57, 240, s)-Nets in Base 2

(240−57, 240, 195)-Net over F₂ — Constructive and digital

Digital (183, 240, 195)-net over F₂, using

t-expansion [i] based on digital (182, 240, 195)-net over F₂, using
- 12 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 84, 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]

(240−57, 240, 374)-Net over F₂ — Digital

Digital (183, 240, 374)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−57, 240, 4151)-Net in Base 2 — Upper bound on s

There is no (183, 240, 4152)-net in base 2, because

1 times m-reduction [i] would yield (183, 239, 4152)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 886060 031071 993286 916967 601225 714780 211990 985563 201934 396956 960431 955260 > 2²³⁹ [i]