MinT - Best Known (259−60, 259, s)-Nets in Base 2

Best Known (259−60, 259, s)-Nets in Base 2

(259−60, 259, 205)-Net over F₂ — Constructive and digital

Digital (199, 259, 205)-net over F₂, using

2¹ times duplication [i] based on digital (198, 258, 205)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 36, 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 (162, 222, 195)-net over F₂, using
    - trace code for nets [i] based on digital (14, 74, 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]

(259−60, 259, 427)-Net over F₂ — Digital

Digital (199, 259, 427)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−60, 259, 4738)-Net in Base 2 — Upper bound on s

There is no (199, 259, 4739)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 929393 035614 087337 733898 999402 169039 778477 097758 014484 770682 843002 553430 045024 > 2²⁵⁹ [i]