MinT - Best Known (201, 249, s)-Nets in Base 2

Best Known (201, 249, s)-Nets in Base 2

(201, 249, 272)-Net over F₂ — Constructive and digital

Digital (201, 249, 272)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 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 (168, 216, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 54, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(201, 249, 698)-Net over F₂ — Digital

Digital (201, 249, 698)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(201, 249, 12982)-Net in Base 2 — Upper bound on s

There is no (201, 249, 12983)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 905 152392 566336 359626 038885 612719 305939 871594 405517 100064 765864 757535 013652 > 2²⁴⁹ [i]