MinT - Best Known (196−36, 196, s)-Nets in Base 2

Best Known (196−36, 196, s)-Nets in Base 2

(196−36, 196, 320)-Net over F₂ — Constructive and digital

Digital (160, 196, 320)-net over F₂, using

2¹ times duplication [i] based on digital (159, 195, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 39, 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]

(196−36, 196, 677)-Net over F₂ — Digital

Digital (160, 196, 677)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−36, 196, 14295)-Net in Base 2 — Upper bound on s

There is no (160, 196, 14296)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100458 288605 620367 998144 414930 587729 261979 763608 642245 590213 > 2¹⁹⁶ [i]