MinT - Best Known (252−52, 252, s)-Nets in Base 2

Best Known (252−52, 252, s)-Nets in Base 2

(252−52, 252, 260)-Net over F₂ — Constructive and digital

Digital (200, 252, 260)-net over F₂, using

t-expansion [i] based on digital (198, 252, 260)-net over F₂, using
- 4 times m-reduction [i] based on digital (198, 256, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 64, 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]

(252−52, 252, 573)-Net over F₂ — Digital

Digital (200, 252, 573)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−52, 252, 8690)-Net in Base 2 — Upper bound on s

There is no (200, 252, 8691)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7244 432254 245292 178808 761516 265275 945628 647259 102968 049750 948148 186235 015828 > 2²⁵² [i]