MinT - Best Known (255−53, 255, s)-Nets in Base 2

Best Known (255−53, 255, s)-Nets in Base 2

(255−53, 255, 260)-Net over F₂ — Constructive and digital

Digital (202, 255, 260)-net over F₂, using

t-expansion [i] based on digital (201, 255, 260)-net over F₂, using
- 5 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]

(255−53, 255, 567)-Net over F₂ — Digital

Digital (202, 255, 567)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−53, 255, 9168)-Net in Base 2 — Upper bound on s

There is no (202, 255, 9169)-net in base 2, because

1 times m-reduction [i] would yield (202, 254, 9169)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28971 820950 019783 093149 050045 747636 630946 786527 958041 825142 693803 541933 978560 > 2²⁵⁴ [i]