MinT - Best Known (192−63, 192, s)-Nets in Base 2

Best Known (192−63, 192, s)-Nets in Base 2

(192−63, 192, 112)-Net over F₂ — Constructive and digital

Digital (129, 192, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 96, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(192−63, 192, 140)-Net over F₂ — Digital

Digital (129, 192, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−63, 192, 843)-Net in Base 2 — Upper bound on s

There is no (129, 192, 844)-net in base 2, because

1 times m-reduction [i] would yield (129, 191, 844)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3162 592774 475034 059535 663595 586796 239774 408780 919926 650800 > 2¹⁹¹ [i]