MinT - Best Known (257−56, 257, s)-Nets in Base 2

Best Known (257−56, 257, s)-Nets in Base 2

(257−56, 257, 260)-Net over F₂ — Constructive and digital

Digital (201, 257, 260)-net over F₂, using

3 times m-reduction [i] based on digital (201, 260, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 65, 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]

(257−56, 257, 499)-Net over F₂ — Digital

Digital (201, 257, 499)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−56, 257, 6505)-Net in Base 2 — Upper bound on s

There is no (201, 257, 6506)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 232140 287833 898911 020051 301181 419307 519280 280166 651164 757381 104168 954774 130136 > 2²⁵⁷ [i]