MinT - Best Known (170, 170+44, s)-Nets in Base 2

Best Known (170, 170+44, s)-Nets in Base 2

(170, 170+44, 260)-Net over F₂ — Constructive and digital

Digital (170, 214, 260)-net over F₂, using

t-expansion [i] based on digital (168, 214, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (168, 216, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 54, 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]

(170, 170+44, 505)-Net over F₂ — Digital

Digital (170, 214, 505)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 170+44, 7642)-Net in Base 2 — Upper bound on s

There is no (170, 214, 7643)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26393 821987 205380 831337 134728 224898 891331 700951 998651 480925 265366 > 2²¹⁴ [i]