MinT - Best Known (259−55, 259, s)-Nets in Base 2

Best Known (259−55, 259, s)-Nets in Base 2

(259−55, 259, 260)-Net over F₂ — Constructive and digital

Digital (204, 259, 260)-net over F₂, using

t-expansion [i] based on digital (201, 259, 260)-net over F₂, using
- 1 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]

(259−55, 259, 540)-Net over F₂ — Digital

Digital (204, 259, 540)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−55, 259, 8180)-Net in Base 2 — Upper bound on s

There is no (204, 259, 8181)-net in base 2, because

1 times m-reduction [i] would yield (204, 258, 8181)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 463293 297720 975298 593558 390818 221930 279606 476058 531096 479960 069952 906278 505216 > 2²⁵⁸ [i]