MinT - Best Known (245−56, 245, s)-Nets in Base 2

Best Known (245−56, 245, s)-Nets in Base 2

(245−56, 245, 205)-Net over F₂ — Constructive and digital

Digital (189, 245, 205)-net over F₂, using

2¹ times duplication [i] based on digital (188, 244, 205)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 34, 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 (154, 210, 195)-net over F₂, using
    - trace code for nets [i] based on digital (14, 70, 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]

(245−56, 245, 421)-Net over F₂ — Digital

Digital (189, 245, 421)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−56, 245, 4822)-Net in Base 2 — Upper bound on s

There is no (189, 245, 4823)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56 562131 923064 597739 303226 525442 792270 527714 801473 392338 672371 697477 173912 > 2²⁴⁵ [i]