MinT - Best Known (254−48, 254, s)-Nets in Base 2

Best Known (254−48, 254, s)-Nets in Base 2

(254−48, 254, 275)-Net over F₂ — Constructive and digital

Digital (206, 254, 275)-net over F₂, using

2¹ times duplication [i] based on digital (205, 253, 275)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 37, 15)-net over F₂, using
    - net from sequence [i] based on digital (13, 14)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 13 and N(F) ≥ 15, 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]

(254−48, 254, 757)-Net over F₂ — Digital

Digital (206, 254, 757)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−48, 254, 15005)-Net in Base 2 — Upper bound on s

There is no (206, 254, 15006)-net in base 2, because

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]