MinT - Best Known (206, 206+42, s)-Nets in Base 2

Best Known (206, 206+42, s)-Nets in Base 2

(206, 206+42, 490)-Net over F₂ — Constructive and digital

Digital (206, 248, 490)-net over F₂, using

2³ times duplication [i] based on digital (203, 245, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 49, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(206, 206+42, 1086)-Net over F₂ — Digital

Digital (206, 248, 1086)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206, 206+42, 31122)-Net in Base 2 — Upper bound on s

There is no (206, 248, 31123)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 452 316154 415980 183002 272843 553654 685200 644531 164181 900565 020617 897008 584144 > 2²⁴⁸ [i]