MinT - Best Known (170, 170+47, s)-Nets in Base 2

Best Known (170, 170+47, s)-Nets in Base 2

(170, 170+47, 260)-Net over F₂ — Constructive and digital

Digital (170, 217, 260)-net over F₂, using

2¹ times duplication [i] based on digital (169, 216, 260)-net over F₂, using
- t-expansion [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+47, 439)-Net over F₂ — Digital

Digital (170, 217, 439)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 170+47, 6297)-Net in Base 2 — Upper bound on s

There is no (170, 217, 6298)-net in base 2, because

1 times m-reduction [i] would yield (170, 216, 6298)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105393 853848 014121 556834 891614 982508 157044 785906 219685 102024 266828 > 2²¹⁶ [i]