MinT - Best Known (195−36, 195, s)-Nets in Base 2

Best Known (195−36, 195, s)-Nets in Base 2

(195−36, 195, 320)-Net over F₂ — Constructive and digital

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]

(195−36, 195, 663)-Net over F₂ — Digital

Digital (159, 195, 663)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−36, 195, 13754)-Net in Base 2 — Upper bound on s

There is no (159, 195, 13755)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50232 252784 794065 811803 822871 210525 854913 874401 336573 070793 > 2¹⁹⁵ [i]