MinT - Best Known (227−48, 227, s)-Nets in Base 2

Best Known (227−48, 227, s)-Nets in Base 2

(227−48, 227, 260)-Net over F₂ — Constructive and digital

Digital (179, 227, 260)-net over F₂, using

t-expansion [i] based on digital (177, 227, 260)-net over F₂, using
- 1 times m-reduction [i] based on digital (177, 228, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 57, 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]

(227−48, 227, 488)-Net over F₂ — Digital

Digital (179, 227, 488)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−48, 227, 6860)-Net in Base 2 — Upper bound on s

There is no (179, 227, 6861)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 215 902794 846613 575487 258289 966884 848829 132090 968029 946812 962064 587204 > 2²²⁷ [i]