MinT - Best Known (206, 255, s)-Nets in Base 2

Best Known (206, 255, s)-Nets in Base 2

(206, 255, 274)-Net over F₂ — Constructive and digital

Digital (206, 255, 274)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (11, 35, 14)-net over F₂, using
  - net from sequence [i] based on digital (11, 13)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
2. digital (171, 220, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 55, 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]

(206, 255, 719)-Net over F₂ — Digital

Digital (206, 255, 719)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206, 255, 15005)-Net in Base 2 — Upper bound on s

There is no (206, 255, 15006)-net in base 2, because

1 times m-reduction [i] would yield (206, 254, 15006)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28990 478639 105658 811115 797214 501271 159123 773412 131363 197079 825284 618055 704603 > 2²⁵⁴ [i]