MinT - Best Known (212, 256, s)-Nets in Base 2

Best Known (212, 256, s)-Nets in Base 2

(212, 256, 490)-Net over F₂ — Constructive and digital

Digital (212, 256, 490)-net over F₂, using

2¹ 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]

(212, 256, 1055)-Net over F₂ — Digital

Digital (212, 256, 1055)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(212, 256, 28791)-Net in Base 2 — Upper bound on s

There is no (212, 256, 28792)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 115874 289526 713733 315619 483212 460596 456161 415439 831891 016295 907771 566666 087301 > 2²⁵⁶ [i]