MinT - Best Known (188, 188+56, s)-Nets in Base 2

Best Known (188, 188+56, s)-Nets in Base 2

(188, 188+56, 205)-Net over F₂ — Constructive and digital

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]

(188, 188+56, 415)-Net over F₂ — Digital

Digital (188, 244, 415)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(188, 188+56, 4703)-Net in Base 2 — Upper bound on s

There is no (188, 244, 4704)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 270331 877675 973637 280283 078682 531811 475232 307128 107142 580677 179262 987435 > 2²⁴⁴ [i]