MinT - Best Known (206−56, 206, s)-Nets in Base 2

Best Known (206−56, 206, s)-Nets in Base 2

(206−56, 206, 144)-Net over F₂ — Constructive and digital

Digital (150, 206, 144)-net over F₂, using

t-expansion [i] based on digital (149, 206, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (149, 207, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 69, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(206−56, 206, 232)-Net over F₂ — Digital

Digital (150, 206, 232)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−56, 206, 1811)-Net in Base 2 — Upper bound on s

There is no (150, 206, 1812)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 967130 651222 884751 097578 756491 051419 458755 794822 199171 202240 > 2²⁰⁶ [i]