MinT - Best Known (257−44, 257, s)-Nets in Base 2

Best Known (257−44, 257, s)-Nets in Base 2

(257−44, 257, 490)-Net over F₂ — Constructive and digital

Digital (213, 257, 490)-net over F₂, using

2² times duplication [i] based on digital (211, 255, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 51, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(257−44, 257, 1073)-Net over F₂ — Digital

Digital (213, 257, 1073)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−44, 257, 29713)-Net in Base 2 — Upper bound on s

There is no (213, 257, 29714)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231642 062954 343771 976340 810064 519392 262752 205042 288302 607751 859210 563115 901696 > 2²⁵⁷ [i]