MinT - Best Known (252−58, 252, s)-Nets in Base 2

Best Known (252−58, 252, s)-Nets in Base 2

(252−58, 252, 205)-Net over F₂ — Constructive and digital

Digital (194, 252, 205)-net over F₂, using

2¹ times duplication [i] based on digital (193, 251, 205)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 35, 10)-net over F₂, using
    - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
  2. digital (158, 216, 195)-net over F₂, using
    - trace code for nets [i] based on digital (14, 72, 65)-net over F₈, using
      - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(252−58, 252, 424)-Net over F₂ — Digital

Digital (194, 252, 424)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−58, 252, 4776)-Net in Base 2 — Upper bound on s

There is no (194, 252, 4777)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7267 223883 156406 302688 080199 050905 818404 151787 276743 880553 478653 821315 256304 > 2²⁵² [i]