MinT - Best Known (197, 197+58, s)-Nets in Base 2

Best Known (197, 197+58, s)-Nets in Base 2

(197, 197+58, 207)-Net over F₂ — Constructive and digital

Digital (197, 255, 207)-net over F₂, using

2¹ times duplication [i] based on digital (196, 254, 207)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 38, 12)-net over F₂, using
    - net from sequence [i] based on digital (9, 11)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, 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]

(197, 197+58, 442)-Net over F₂ — Digital

Digital (197, 255, 442)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197, 197+58, 5134)-Net in Base 2 — Upper bound on s

There is no (197, 255, 5135)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 58044 971205 497784 284517 688564 039284 373869 577113 398671 789050 754417 064021 398272 > 2²⁵⁵ [i]