MinT - Best Known (256−52, 256, s)-Nets in Base 2

Best Known (256−52, 256, s)-Nets in Base 2

(256−52, 256, 260)-Net over F₂ — Constructive and digital

Digital (204, 256, 260)-net over F₂, using

t-expansion [i] based on digital (201, 256, 260)-net over F₂, using
- 4 times m-reduction [i] based on digital (201, 260, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 65, 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]

(256−52, 256, 608)-Net over F₂ — Digital

Digital (204, 256, 608)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−52, 256, 9672)-Net in Base 2 — Upper bound on s

There is no (204, 256, 9673)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 115809 490884 464457 708404 706645 078083 525529 818057 819767 570612 059840 869248 240912 > 2²⁵⁶ [i]