MinT - Best Known (196, 196+58, s)-Nets in Base 2

Best Known (196, 196+58, s)-Nets in Base 2

(196, 196+58, 207)-Net over F₂ — Constructive and digital

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]

(196, 196+58, 436)-Net over F₂ — Digital

Digital (196, 254, 436)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196, 196+58, 5012)-Net in Base 2 — Upper bound on s

There is no (196, 254, 5013)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 29070 390622 192070 127917 236224 882538 172941 984111 181641 030886 217102 826488 882208 > 2²⁵⁴ [i]