MinT - Best Known (171−41, 171, s)-Nets in Base 2

Best Known (171−41, 171, s)-Nets in Base 2

(171−41, 171, 195)-Net over F₂ — Constructive and digital

Digital (130, 171, 195)-net over F₂, using

3 times m-reduction [i] based on digital (130, 174, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 58, 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]

(171−41, 171, 274)-Net over F₂ — Digital

Digital (130, 171, 274)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−41, 171, 2977)-Net in Base 2 — Upper bound on s

There is no (130, 171, 2978)-net in base 2, because

1 times m-reduction [i] would yield (130, 170, 2978)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1505 252532 356813 515566 181213 247376 145197 228347 827496 > 2¹⁷⁰ [i]