MinT - Best Known (257−48, 257, s)-Nets in Base 2

Best Known (257−48, 257, s)-Nets in Base 2

(257−48, 257, 320)-Net over F₂ — Constructive and digital

Digital (209, 257, 320)-net over F₂, using

2² times duplication [i] based on digital (207, 255, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 51, 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]

(257−48, 257, 794)-Net over F₂ — Digital

Digital (209, 257, 794)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−48, 257, 16366)-Net in Base 2 — Upper bound on s

There is no (209, 257, 16367)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231799 854622 277012 332211 661697 327566 076742 578565 947955 724052 628831 113035 941666 > 2²⁵⁷ [i]