MinT - Best Known (53, 53+26, s)-Nets in Base 2

Best Known (53, 53+26, s)-Nets in Base 2

(53, 53+26, 60)-Net over F₂ — Constructive and digital

Digital (53, 79, 60)-net over F₂, using

1 times m-reduction [i] based on digital (53, 80, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 40, 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]

(53, 53+26, 70)-Net over F₂ — Digital

Digital (53, 79, 70)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+26, 364)-Net in Base 2 — Upper bound on s

There is no (53, 79, 365)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 625084 522749 878300 004978 > 2⁷⁹ [i]