MinT - Best Known (196−43, 196, s)-Nets in Base 2

Best Known (196−43, 196, s)-Nets in Base 2

(196−43, 196, 260)-Net over F₂ — Constructive and digital

Digital (153, 196, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 49, 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]

(196−43, 196, 389)-Net over F₂ — Digital

Digital (153, 196, 389)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−43, 196, 5386)-Net in Base 2 — Upper bound on s

There is no (153, 196, 5387)-net in base 2, because

1 times m-reduction [i] would yield (153, 195, 5387)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50366 221351 813735 650655 533283 723800 133629 576285 509178 028032 > 2¹⁹⁵ [i]