MinT - Best Known (171, 215, s)-Nets in Base 2

Best Known (171, 215, s)-Nets in Base 2

(171, 215, 260)-Net over F₂ — Constructive and digital

Digital (171, 215, 260)-net over F₂, using

5 times m-reduction [i] based on digital (171, 220, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 55, 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]

(171, 215, 514)-Net over F₂ — Digital

Digital (171, 215, 514)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 215, 7887)-Net in Base 2 — Upper bound on s

There is no (171, 215, 7888)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 52688 680003 594438 590253 677890 578638 028612 732099 870789 848132 360732 > 2²¹⁵ [i]