MinT - Best Known (252−48, 252, s)-Nets in Base 2

Best Known (252−48, 252, s)-Nets in Base 2

(252−48, 252, 274)-Net over F₂ — Constructive and digital

Digital (204, 252, 274)-net over F₂, using

2¹ times duplication [i] based on digital (203, 251, 274)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 35, 14)-net over F₂, using
    - net from sequence [i] based on digital (11, 13)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
  2. digital (168, 216, 260)-net over F₂, using
    - trace code for nets [i] based on digital (6, 54, 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]

(252−48, 252, 733)-Net over F₂ — Digital

Digital (204, 252, 733)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−48, 252, 14160)-Net in Base 2 — Upper bound on s

There is no (204, 252, 14161)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7237 948182 519358 713679 865119 725924 418370 749176 532664 885552 792360 552196 213064 > 2²⁵² [i]