MinT - Best Known (175, 225, s)-Nets in Base 2

Best Known (175, 225, s)-Nets in Base 2

(175, 225, 260)-Net over F₂ — Constructive and digital

Digital (175, 225, 260)-net over F₂, using

2¹ times duplication [i] based on digital (174, 224, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 56, 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]

(175, 225, 422)-Net over F₂ — Digital

Digital (175, 225, 422)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 225, 5173)-Net in Base 2 — Upper bound on s

There is no (175, 225, 5174)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 53 967449 737840 932222 533319 757471 845806 930573 204760 986367 505924 866108 > 2²²⁵ [i]