MinT - Best Known (206, 206+46, s)-Nets in Base 2

Best Known (206, 206+46, s)-Nets in Base 2

(206, 206+46, 320)-Net over F₂ — Constructive and digital

Digital (206, 252, 320)-net over F₂, using

2² times duplication [i] based on digital (204, 250, 320)-net over F₂, using
- t-expansion [i] based on digital (203, 250, 320)-net over F₂, using
  - trace code for nets [i] based on digital (3, 50, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]

(206, 206+46, 843)-Net over F₂ — Digital

Digital (206, 252, 843)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206, 206+46, 18702)-Net in Base 2 — Upper bound on s

There is no (206, 252, 18703)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7237 554901 532431 185653 446536 604541 505154 897733 812348 588820 065330 578257 081888 > 2²⁵² [i]