MinT - Best Known (70, 70+42, s)-Nets in Base 2

Best Known (70, 70+42, s)-Nets in Base 2

(70, 70+42, 60)-Net over F₂ — Constructive and digital

Digital (70, 112, 60)-net over F₂, using

2 times m-reduction [i] based on digital (70, 114, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 57, 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]

(70, 70+42, 67)-Net over F₂ — Digital

Digital (70, 112, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+42, 320)-Net in Base 2 — Upper bound on s

There is no (70, 112, 321)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5472 359506 741950 769848 961783 799712 > 2¹¹² [i]