MinT - Best Known (196−45, 196, s)-Nets in Base 2

Best Known (196−45, 196, s)-Nets in Base 2

(196−45, 196, 195)-Net over F₂ — Constructive and digital

Digital (151, 196, 195)-net over F₂, using

t-expansion [i] based on digital (150, 196, 195)-net over F₂, using
- 8 times m-reduction [i] based on digital (150, 204, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 68, 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]

(196−45, 196, 344)-Net over F₂ — Digital

Digital (151, 196, 344)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−45, 196, 4185)-Net in Base 2 — Upper bound on s

There is no (151, 196, 4186)-net in base 2, because

1 times m-reduction [i] would yield (151, 195, 4186)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50402 594049 839752 112851 580762 054205 174051 099243 963745 898236 > 2¹⁹⁵ [i]