MinT - Best Known (154−63, 154, s)-Nets in Base 2

Best Known (154−63, 154, s)-Nets in Base 2

(154−63, 154, 60)-Net over F₂ — Constructive and digital

Digital (91, 154, 60)-net over F₂, using

2 times m-reduction [i] based on digital (91, 156, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 78, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(154−63, 154, 71)-Net over F₂ — Digital

Digital (91, 154, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−63, 154, 336)-Net in Base 2 — Upper bound on s

There is no (91, 154, 337)-net in base 2, because

1 times m-reduction [i] would yield (91, 153, 337)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12026 565973 308736 347378 115425 751317 346415 032320 > 2¹⁵³ [i]