MinT - Best Known (197, 197+54, s)-Nets in Base 2

Best Known (197, 197+54, s)-Nets in Base 2

(197, 197+54, 260)-Net over F₂ — Constructive and digital

Digital (197, 251, 260)-net over F₂, using

t-expansion [i] based on digital (195, 251, 260)-net over F₂, using
- 1 times m-reduction [i] based on digital (195, 252, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 63, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(197, 197+54, 507)-Net over F₂ — Digital

Digital (197, 251, 507)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197, 197+54, 6828)-Net in Base 2 — Upper bound on s

There is no (197, 251, 6829)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3622 102857 782571 195617 762752 966620 244072 341949 441280 057212 315593 782932 685120 > 2²⁵¹ [i]